A123334 a(n) = 4^n*(Gamma(n+1/4)/Gamma(1/4) + (n-1)!).

5, 21, 173, 2121, 34521, 700365, 17017605, 481714065, 15566262705, 565382074005, 22800157775325, 1010786809534425, 48858860891558025, 2557374374022392925, 144098786151306911925, 8696418977823430478625

Offset: 1

Author

Karol A. Penson, Sep 26 2006

Keywords

• nonn

Comments

The EXP-transform of a(n) is equal to A121631(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..365

Crossrefs

Cf. A121631.

Programs

Mathematica

With[{nmax = 50}, CoefficientList[Series[(1 - 4*x)^(-1/4) - 1 - Log[1 - 4*x], {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 12 2017 *)

PARI

x='x+O('x^30); Vec(serlaplace((1-4*x)^(-1/4) - 1 - log(1-4*x))) \\ G. C. Greubel, Oct 12 2017

Formula

E.g.f.: (1-4*x)^(-1/4) - 1 - log(1-4*x).

a(n) = A007696(n) + A000302(n)*A000142(n-1). - R. J. Mathar, Jun 18 2009, Jul 07 2009