OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2019
STATUS
approved