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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
OFFSET
0,3
COMMENTS
Differs from A005651 first at n = 7: a(n) = 11271 < 11481 = A005651(7).
LINKS
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.
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2019
STATUS
approved