A126444 a(n) = Sum_{k=0..n-1} C(n-1,k)*a(k)*a(n-1-k)*2^k for n>0, with a(0)=1.

1, 1, 3, 19, 225, 4801, 185523, 13298659, 1815718305, 481790947681, 251592291767043, 260427247041910099, 536497603929547755585, 2204489516030261302702561, 18090090482887693483393912563, 296659627048147988400872084439139

Offset: 0

Author

Paul D. Hanna, Jan 01 2007

Keywords

• nonn

Comments

Generated by a generalization of a recurrence for the factorials.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A126470.

Programs

Mathematica

b = ConstantArray[0,21]; b[[1]]=1; b[[2]]=1; Do[b[[n+1]] = Sum[Binomial[n-1,k]*b[[k+1]]*b[[n-k]]*2^k,{k,0,n-1}],{n,2,20}]; b  (* Vaclav Kotesovec, Feb 23 2014 *)

PARI

a(n)=if(n==0,1,sum(k=0,n-1,binomial(n-1,k)*a(k)*a(n-1-k)*2^k))

PARI

{a(n)=local(A=1+x);for(i=0,n,A=1+intformal(A*subst(A,x,2*x+x*O(x^n))));n!*polcoeff(A,n,x)} \\ Paul D. Hanna, Nov 22 2008

Formula

a(n) = Sum_{k=0..n*(n-1)/2} A126470(n,k)*2^k.

E.g.f. satisfies: A'(x) = A(x)*A(2x) with A(0)=1; the logarithmic derivative of e.g.f. A(x) equals A(2x). - Paul D. Hanna, Nov 22 2008

a(n) ~ c * 2^(n*(n-1)/2), where c = 7.32081762965209017732559... - Vaclav Kotesovec, Feb 23 2014

Extensions

More terms from Vincenzo Librandi, Feb 25 2014