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multinomial_coeff

Run Example
(%i1)load(functs);
(%o1)      /usr/share/maxima/5.21.1/share/simplification/functs.mac
(%i2) length(permutations([m, i, s, s, i, s, i, p, i]));
(%o2)                                2520
(%i3) multinomial_coeff(4, 3, 1, 1);
(%o3)                                2520
(%i4) multinomial(9,[4, 3, 1, 1]);
resolvante 
generale 
 
NOTE: To compile the system do 
load("sym/compile"); 
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
(%o4)                                2520
(%i5) 11!/(4!*4!*2!*1!);
(%o5)                                34650
(%i6) multinomial(11, [4, 4, 2, 1]);
(%o6)                                34650
(%i7) multinomial_coeff(4, 4, 2, 1);
(%o7)                                34650
(%i8) permutations([t, o, o, l]);
(%o8) {[l, o, o, t], [l, o, t, o], [l, t, o, o], [o, l, o, t], [o, l, t, o], 
[o, o, l, t], [o, o, t, l], [o, t, l, o], [o, t, o, l], [t, l, o, o], 
[t, o, l, o], [t, o, o, l]}
(%i9) length(permutations([t, o, o, l]));
(%o9)                                 12
(%i10) permutation(4, 2);
(%o10)                                12
(%i11) multinomial(4, [1, 2, 1]);
(%o11)                                12
(%i12) multinomial_coeff(1, 2, 1);
(%o12)                                12
(%i13) makelist(makelist([x, y], y, 1, 10), x, 1, 10);
(%o13) [[[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], 
[1, 9], [1, 10]], [[2, 1], [2, 2], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], 
[2, 8], [2, 9], [2, 10]], [[3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6], 
[3, 7], [3, 8], [3, 9], [3, 10]], [[4, 1], [4, 2], [4, 3], [4, 4], [4, 5], 
[4, 6], [4, 7], [4, 8], [4, 9], [4, 10]], 
[[5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8], [5, 9], 
[5, 10]], [[6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6], [6, 7], [6, 8], 
[6, 9], [6, 10]], [[7, 1], [7, 2], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7], 
[7, 8], [7, 9], [7, 10]], [[8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], 
[8, 7], [8, 8], [8, 9], [8, 10]], [[9, 1], [9, 2], [9, 3], [9, 4], [9, 5], 
[9, 6], [9, 7], [9, 8], [9, 9], [9, 10]], 
[[10, 1], [10, 2], [10, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], 
[10, 9], [10, 10]]]
(%i14) 
Run Example
multinomial_coeff (a, b, c);
                                 (c + b + a)!
(%o1)                            ------------
                                   a! b! c!
(%i2) 
Run Example
multinomial_coeff (77,99,44,66);
(%o1) 444088892561466722603287930820331084166788716638528367798180958610212896\
751831350501287344089871184481179546569475781461810785122226035230442664083152\
70137956000000
(%i2) 

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