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A327827 Sum of multinomials M(n; lambda), where lambda ranges over all partitions of n into parts incorporating 1. 3
0, 1, 2, 9, 40, 235, 1476, 11214, 91848, 859527, 8710300, 97675138, 1179954612, 15490520786, 217602374458, 3280028076615, 52571985879600, 895913825750191, 16140560853800556, 307048409240931810, 6143666813617775100, 129096480664676773542, 2840750997343361802150 (list; graph; refs; listen; history; text; internal format)
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);

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

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)