A325308 Sum of all distinct multinomial coefficients M(n;lambda), where lambda ranges over the partitions of n.

1, 1, 3, 10, 47, 246, 1602, 11271, 93767, 847846, 8618738, 94966191, 1149277802, 14946737339, 210112991441, 3152429219400, 50538450211103, 859238687076542, 15481605986593038, 294161321911723167, 5886118362589143742, 123610854463260840735, 2720101086040978435931

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-François Alcover, May 06 2020, after Maple *)

Crossrefs

Column k=1 of A325305.

Cf. A005651.

Sequence in context: A346188 A226875 A226876 * A226877 A226878 A226879

Adjacent sequences: A325305 A325306 A325307 * A325309 A325310 A325311

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2019

Status

approved