%I #15 Aug 20 2021 07:02:41
%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 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
%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