A094856 E.g.f.: exp(4x)/(1-4x)^(1/4).

1, 5, 29, 217, 2297, 34349, 674965, 16276481, 461527793, 14993138773, 548258687501, 22272738733865, 994870668959209, 48451779617935997, 2554818339078836357, 144990720049391354449, 8811240401831517313505, 570857963393730507892901, 39275973938444154366908413

Offset: 0

Author

Philippe Deléham, Jun 13 2004

Keywords

• nonn

Comments

Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n) for x = 1, 2, 3 respectively.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Programs

Mathematica

Table[n!*SeriesCoefficient[E^(4x)/(1-4x)^(1/4),{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 03 2012 *)
With[{nn=20},CoefficientList[Series[Exp[4x]/(1-4x)^(1/4),{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Mar 29 2013 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(4*x)/(1-4*x)^(1/4))) \\ Joerg Arndt, May 11 2013

Formula

a(n) = Sum_{k = 0..n} A046716(n, k)*4^k.

a(n) ~ n^(n-1/4)*4^n*Gamma(3/4)/(exp(n-1)*sqrt(Pi)). - Vaclav Kotesovec, Oct 03 2012

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

Extensions

Corrected and extended by Harvey P. Dale, Mar 29 2013