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%I #43 May 10 2022 14:13:52
%S 1,5,26,142,824,5144,34960,261104,2154368,19651456,197563136,
%T 2177388800,26145442816,339957865472,4759678552064,71396252022784,
%U 1142344327331840,19419870744510464,349557742120665088,6641597375170543616,132831948602922500096
%N E.g.f.: exp(4x)/(1-x).
%C a(n) is the binomial transform of A053486. More generally, for every integer k, the sequence whose e.g.f is exp((k+1)*x)/(1-x) is the binomial transform of the sequence whose e.g.f is exp(k*x)/(1-x). - _Groux Roland_, Mar 23 2011
%H Vincenzo Librandi, <a href="/A053487/b053487.txt">Table of n, a(n) for n = 0..200</a>
%H J. W. Layman, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL4/LAYMAN/hankel.html">The Hankel Transform and Some of its Properties</a>, J. Integer Sequences, 4 (2001), #01.1.5.
%F a(n) is the permanent of the n X n matrix with 5's on the diagonal and 1's elsewhere. a(n) = Sum_{k=0..n} A008290(n, k)*5^k. - _Philippe Deléham_, Dec 12 2003
%F E.g.f.: exp(4x)/(1-x)=1/E(0); E(k)=1-x/(1-4/(4+(k+1)/E(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Nov 21 2011
%F G.f.: 1/Q(0), where Q(k)= 1 - 4*x - x*(k+1)/(1-x*(k+1)/Q(k+1)); (continued fraction). - _Sergei N. Gladkovskii_, Apr 19 2013
%F a(n) ~ n! * exp(4). - _Vaclav Kotesovec_, Jun 21 2013
%F a(n) = exp(4)*Gamma(n+1,4). - _Gerry Martens_, Jul 24 2015
%F a(n) = KummerU(-n, -n, 4). - _Peter Luschny_, May 10 2022
%p F(x) := exp(4*x)/(1-x): f[0]:=F(x): for n from 1 to 20 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..20); # _Zerinvary Lajos_, Apr 03 2009
%p seq(simplify(KummerU(-n, -n, 4)), n = 0..20); # _Peter Luschny_, May 10 2022
%t With[{nn=30},CoefficientList[Series[Exp[4x]/(1-x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jun 09 2013 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jan 15 2000
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