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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..14

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

Formula

a(n) = Product_{k=1..A000041(n)} A036038(n,k).

a(n) = A309951(n,A000041(n)).

Example

a(3) = M(3;3) * M(3;2,1) * M(3;1,1,1) = 1 * 3 * 6 = 18.

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 *)

Crossrefs

Rightmost terms in rows of A309951.

Cf. A000041, A005651, A036038, A078760, A210237.

Sequence in context: A006262 A003043 A059783 * A208056 A276092 A191554

Adjacent sequences: A309969 A309970 A309971 * A309973 A309974 A309975

Keyword

nonn

Author

Alois P. Heinz, Aug 25 2019

Status

approved