OFFSET
0,4
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..125
Wikipedia, Multinomial coefficients
Wikipedia, Partition (number theory)
MAPLE
g:= proc(n, i) option remember; `if`(i*(i+1)/2<n, {}, `if`(n=0, {1},
{map(x->binomial(n, i)*x, g(n-i, min(n-i, i-1)))[], g(n, i-1)[]}))
end:
a:= n-> nops(g(n$2)):
seq(a(n), n=0..55);
MATHEMATICA
g[n_, i_] := g[n, i] = If[i(i+1)/2 < n, {}, If[n == 0, {1}, Union[ Binomial[n, i] #& /@ g[n - i, Min[n - i, i - 1]], g[n, i - 1]]]];
a[n_] := Length[g[n, n]];
a /@ Range[0, 55] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 26 2019
STATUS
approved