A309972 Product of multinomial coefficients M(n;lambda), where lambda ranges over all partitions of n.
1, 1, 2, 18, 6912, 216000000, 1632586752000000000, 498266101635303733401600000000000, 1140494258799407218656986754465090350453096448000000000000000
Offset: 0
Keywords
Examples
a(3) = M(3;3) * M(3;2,1) * M(3;1,1,1) = 1 * 3 * 6 = 18.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..14
- Wikipedia, Multinomial coefficients
- Wikipedia, Partition (number theory)
Programs
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Maple
b:= proc(n, i) option remember; `if`(n=0 or i=1, [n!], [map(t-> binomial(n, i)*t, b(n-i, min(n-i, i)))[], b(n, i-1)[]]) end: a:= n-> mul(i, i=b(n$2)): seq(a(n), n=0..9); # Alois P. Heinz, Aug 25 2019 -
Mathematica
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, {n!}, Join[Binomial[n, i] #& /@ b[n - i, Min[n - i, i]], b[n, i - 1]]]; a[n_] := Times @@ b[n, n]; a /@ Range[0, 9] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)