OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: Product_{j>=1} (1+x^j)^A049401(j).
MAPLE
g:= proc(n) option remember;
`if`(n<3, [1, 1, 2][n+1], ((3*n^2+17*n+15)*g(n-1)
+(n-1)*(13*n+9)*g(n-2) -15*(n-1)*(n-2)*g(n-3)) /
((n+4)*(n+6)))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(g(i), j), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..35);
MATHEMATICA
g[n_] := g[n] = If[n<3, {1, 1, 2}[[n+1]], ((3*n^2 + 17*n + 15)*g[n-1] + (n-1)*(13*n + 9)*g[n-2] - 15*(n-1)*(n-2)*g[n-3]) / ((n+4)*(n+6))];
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1]* Binomial[g[i], j], {j, 0, n/i}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 06 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 15 2017
STATUS
approved