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A327711 Sum of multinomials M(n-k; p_1-1, ..., p_k-1), where p = (p_1, ..., p_k) ranges over all partitions of n (k is a partition length). 4
1, 1, 2, 3, 6, 10, 27, 55, 171, 475, 1555, 4915, 20023, 68243, 288024, 1213828, 5435935, 23966970, 121432923, 578757824, 3130381590, 16427772974, 91877826663, 519546134163, 3199523135912, 18868494152257, 120274458082095, 772954621249540, 5219747666882153 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..635

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

MAPLE

with(combinat):

a:= n-> add(multinomial(n-nops(p), map(

    x-> x-1, p)[], 0), p=partition(n)):

seq(a(n), n=0..28);

# second Maple program:

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<2, 0,

      b(n, i-1, p)) +b(n-i, min(n-i, i), p-1)/(i-1)!)

    end:

a:= n-> b(n$3):

seq(a(n), n=0..28);

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 2, 0, b[n, i - 1, p]] + b[n - i, Min[n - i, i], p - 1]/(i - 1)!];

a[n_] := b[n, n, n];

a /@ Range[0, 28] (* Jean-Fran├žois Alcover, May 01 2020, from 2nd Maple program *)

CROSSREFS

Cf. A005651, A326493, A327712, A327729.

Sequence in context: A272079 A212606 A192440 * A274964 A054357 A056606

Adjacent sequences:  A327708 A327709 A327710 * A327712 A327713 A327714

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 22 2019

STATUS

approved

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)