

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
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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. 831832 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(ni, min(ni, i)))[], g(n, i1)[]})
end:
a:= n> add(i, i=g(n$2)):
seq(a(n), n=0..23);


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



