OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..100
FORMULA
a(n) = A244372(2n+1,n).
a(n) ~ c * d^n / sqrt(n), where d = 2.955765285651994974714817524... is the Otter's rooted tree constant (see A051491), and c = 2.806733... . - Vaclav Kotesovec, Jul 11 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-> `if`(n=0, 1, b(2*n$2, n$2)-b(2*n$2, n-1$2)):
seq(a(n), n=0..30);
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_] := If[n == 0, 1, b[2*n, 2 n, n, n] - b[2*n, 2 n, n - 1, n - 1]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 06 2015, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved