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

0,3

Comments

Generated by a generalization of a recurrence for the factorials.

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A126470.

Sequence in context: A136504 A003111 A160888 * A198046 A295812 A228229

Adjacent sequences: A126441 A126442 A126443 * A126445 A126446 A126447

Keyword

nonn

Author

Paul D. Hanna, Jan 01 2007

Extensions

More terms from Vincenzo Librandi, Feb 25 2014

Status

approved