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