A327827 Sum of multinomials M(n; lambda), where lambda ranges over all partitions of n into parts incorporating 1.

0, 1, 2, 9, 40, 235, 1476, 11214, 91848, 859527, 8710300, 97675138, 1179954612, 15490520786, 217602374458, 3280028076615, 52571985879600, 895913825750191, 16140560853800556, 307048409240931810, 6143666813617775100, 129096480664676773542, 2840750997343361802150

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

Formula

a(n) ~ c * n!, where c = A247551 = 2.5294774720791526481801161542539542411787... - Vaclav Kotesovec, Sep 28 2019

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1,
     `if`(i>n, 0, b(n, i+1, `if`(i=k, 0, k))+
     `if`(i=k, 0, b(n-i, i, k)*binomial(n, i))))
    end:
a:= n-> b(n, 1, 0)-b(n, 1$2):
seq(a(n), n=0..23);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] + If[i == k, 0, b[n - i, Min[n - i, i], k]/i!]];
T[n_, k_] := n! (b[n, n, 0] - If[k == 0, 0, b[n, n, k]]);
a[n_] := T[n, 1];
a /@ Range[0, 23] (* Jean-François Alcover, Dec 09 2020, after Alois P. Heinz *)

Crossrefs

Column k=1 of A327801.

Sequence in context: A261047 A052846 A293152 * A056844 A220471 A213095

Adjacent sequences: A327824 A327825 A327826 * A327828 A327829 A327830

Keyword

nonn

Author

Alois P. Heinz, Sep 26 2019

Status

approved