A135754 E.g.f.: A(x) = Sum_{n>=0} exp((4^n-1)/3*x)*x^n/n!.

1, 1, 3, 19, 239, 6091, 305023, 30818299, 6155906879, 2484667187371, 1989929726352863, 3221489148102557179, 10362312712649347408159, 67345216546226371822133611, 869978904614825017953532433663

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..80

Formula

a(n) = Sum_{k=0..n} C(n,k)*[(4^k-1)/3]^(n-k).

a(n) ~ c * 2^(n^2/2+n+1/2)/(3^(n/2)*sqrt(Pi*n)), where c = Sum_{k = -infinity..infinity} 3^k*4^(-k^2) = 1.86902676808473931... if n is even and c = Sum_{k = -infinity..infinity} 3^(k+1/2)*4^(-(k+1/2)^2) = 1.87384213421283135... if n is odd. - Vaclav Kotesovec, Jun 25 2013

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*((4^k-1)/3)^(n-k), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jun 25 2013 *)

Prog

(PARI) a(n)=sum(k=0, n, binomial(n, k)*((4^k-1)/3)^(n-k))
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp((4^k-1)/3*x)*x^k/k!), n)

Crossrefs

Cf. variants: A001831, A135753.

Sequence in context: A230316 A157675 A355216 * A340225 A118023 A054590

Adjacent sequences: A135751 A135752 A135753 * A135755 A135756 A135757

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2007

Status

approved