A135753 E.g.f.: A(x) = Sum_{n>=0} exp((3^n-1)/2*x)*x^n/n!.

1, 1, 3, 16, 153, 2536, 72513, 3571156, 303033153, 44411895376, 11247688063233, 4933176144494236, 3746180187749948193, 4933259445571307491096, 11257237602638666745470913, 44566655569041016108120599556

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..85

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*[(3^k-1)/2]^(n-k).

a(n) ~ c * 3^(n^2/4)*2^((n+1)/2)/sqrt(Pi*n), where c = Sum_{k = -infinity..infinity} 2^k*3^(-k^2) = 1.8862156350800186... if n is even and c = Sum_{k = -infinity..infinity} 2^(k+1/2)*3^(-(k+1/2)^2) = 1.8865940733664341... if n is odd. - Vaclav Kotesovec, Jun 25 2013

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*((3^k-1)/2)^(n-k), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jun 25 2013 *)

Prog

(PARI) a(n)=sum(k=0, n, binomial(n, k)*((3^k-1)/2)^(n-k))
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp((3^k-1)/2*x)*x^k/k!), n)

Crossrefs

Cf. variants: A001831, A135754.

Sequence in context: A086371 A229954 A228513 * A191959 A349591 A091146

Adjacent sequences: A135750 A135751 A135752 * A135754 A135755 A135756

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2007

Status

approved