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%I #21 Jan 30 2020 21:58:01
%S 1,5,29,217,2297,34349,674965,16276481,461527793,14993138773,
%T 548258687501,22272738733865,994870668959209,48451779617935997,
%U 2554818339078836357,144990720049391354449,8811240401831517313505,570857963393730507892901,39275973938444154366908413
%N E.g.f.: exp(4x)/(1-4x)^(1/4).
%C Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n) for x = 1, 2, 3 respectively.
%H Vincenzo Librandi, <a href="/A094856/b094856.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum_{k = 0..n} A046716(n, k)*4^k.
%F a(n) ~ n^(n-1/4)*4^n*Gamma(3/4)/(exp(n-1)*sqrt(Pi)). - _Vaclav Kotesovec_, Oct 03 2012
%F Conjectured to be D-finite with recurrence: a(n) +(-4*n-1)*a(n-1) +16*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 15 2019
%t Table[n!*SeriesCoefficient[E^(4x)/(1-4x)^(1/4),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 03 2012 *)
%t With[{nn=20},CoefficientList[Series[Exp[4x]/(1-4x)^(1/4),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Mar 29 2013 *)
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(4*x)/(1-4*x)^(1/4))) \\ _Joerg Arndt_, May 11 2013
%K nonn
%O 0,2
%A _Philippe Deléham_, Jun 13 2004
%E Corrected and extended by _Harvey P. Dale_, Mar 29 2013
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