A097815 E.g.f. exp(4x)/(1-4x).

1, 8, 80, 1024, 16640, 333824, 8015872, 224460800, 7182811136, 258581463040, 10343259570176, 455103425282048, 21844964430315520, 1135938150443515904, 63612536425105326080, 3816752185507393306624, 244272139872477466591232

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

Formula

a(n) = 4n*a(n-1)+4^n, n>0, a(0)=1; a(n) = 4^n*A000522(n).

G.f.: 1/Q(0), where Q(k) = 1 - 8*x*(k+1) - 16*x^2*(k+1)^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Sep 30 2013

D-finite with recurrence a(n) +4*(-n-1)*a(n-1) +16*(n-1)*a(n-2)=0. - R. J. Mathar, Feb 19 2015

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[4x]/(1-4x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 02 2017 *)

Crossrefs

Cf. A082032, A097814.

Sequence in context: A228658 A234596 A060375 * A002718 A222825 A057707

Adjacent sequences: A097812 A097813 A097814 * A097816 A097817 A097818

Keyword

easy,nonn

Author

Paul Barry, Aug 26 2004

Status

approved