OFFSET
3,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..1000
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 2.4832535361726368... = A086317 and c = 0.7916031835775118... = A086318. - Vaclav Kotesovec, Jun 27 2014
MAPLE
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 2$2) -`if`(n=0, 0, 1):
seq(a(n), n=3..40);
MATHEMATICA
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[b[i-1, i-1, k, k]+j-1, j]*b[n-i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]] // FullSimplify]; a[n_] := b[n-1, n-1, 2, 2] - If[n == 0, 0, 1]; Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved