OFFSET
0,2
LINKS
FORMULA
G.f.: B(x) - B^2(x)/2 - B(x^2)/2, where B(x) is g.f. for A038077.
a(n) ~ c * d^n / n^(5/2), where d = A246312 = 5.2490324912281705791649522161843092..., c = 0.356142078281568492877259973613... . - Vaclav Kotesovec, Sep 06 2014
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(2*b(i-1$2), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n=0, 1, 2*b(n-1$2) -2*add(b(j-1$2)*b(n-j-1$2)
, j=1..n-1) -`if`(irem(n, 2, 'r')=0, b(r-1$2), 0)):
seq(a(n), n=0..35); # Alois P. Heinz, Aug 02 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[2*b[i-1, i-1], j]*b[n-i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n==0, 1, 2*b[n-1, n-1] - 2*Sum[b[j-1, j-1]*b[n-j-1, n-j-1], {j, 1, n-1}] - If[Mod[n, 2]==0, r=n/2; b[r-1, r-1], 0]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 04 1999
STATUS
approved