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A097815 E.g.f. exp(4x)/(1-4x). 0

%I

%S 1,8,80,1024,16640,333824,8015872,224460800,7182811136,258581463040,

%T 10343259570176,455103425282048,21844964430315520,1135938150443515904,

%U 63612536425105326080,3816752185507393306624,244272139872477466591232

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

%H Michael Z. Spivey and Laura L. Steil, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Spivey/spivey7.html">The k-Binomial Transforms and the Hankel Transform</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

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

%F 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

%F a(n) +4*(-n-1)*a(n-1) +16*(n-1)*a(n-2)=0. - _R. J. Mathar_, Feb 19 2015

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

%Y Cf. A082032, A097814.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Aug 26 2004

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Last modified October 1 11:36 EDT 2020. Contains 337443 sequences. (Running on oeis4.)