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A325308 Sum of all distinct multinomial coefficients M(n;lambda), where lambda ranges over the partitions of n. 2
1, 1, 3, 10, 47, 246, 1602, 11271, 93767, 847846, 8618738, 94966191, 1149277802, 14946737339, 210112991441, 3152429219400, 50538450211103, 859238687076542, 15481605986593038, 294161321911723167, 5886118362589143742, 123610854463260840735, 2720101086040978435931 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Differs from A005651 first at n = 7: a(n) = 11271 < 11481 = A005651(7).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..90

Milton Abramowitz and Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards (Applied Mathematics Series, 55), 1964; see pp. 831-832 for the multinomial coefficients of integer partitions of n = 1..10.

Wikipedia, Multinomial coefficients.

Wikipedia, Partition (number theory).

MAPLE

g:= proc(n, i) option remember; `if`(n=0 or i=1, {n!}, {map(x->

      binomial(n, i)*x, g(n-i, min(n-i, i)))[], g(n, i-1)[]})

    end:

a:= n-> add(i, i=g(n$2)):

seq(a(n), n=0..23);

MATHEMATICA

g[n_, i_] := g[n, i] = If[n == 0 || i == 1, {n!}, Union[Map[Function[x, Binomial[n, i] x], g[n - i, Min[n - i, i]]], g[n, i - 1]]];

a[n_] := Total[g[n, n]];

a /@ Range[0, 23] (* Jean-Fran├žois Alcover, May 06 2020, after Maple *)

CROSSREFS

Column k=1 of A325305.

Cf. A005651.

Sequence in context: A218919 A226875 A226876 * A226877 A226878 A226879

Adjacent sequences:  A325305 A325306 A325307 * A325309 A325310 A325311

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 05 2019

STATUS

approved

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Last modified June 24 11:36 EDT 2021. Contains 345416 sequences. (Running on oeis4.)