OFFSET
10,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 10..700
Wikipedia, Partition of a set
MAPLE
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 11)
end:
a:= n-> coeff(b(n$2, 0), x, 10):
seq(a(n), n=10..30);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[x^j*b[n - i*j, i - 1, p + j]*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2, {j, 0, n/i}]], {x, 0, 11}];
a[n_] := Coefficient[b[n, n, 0], x, 10];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 28 2017
STATUS
approved