A145562 Second column (m=2) of triangle A049029 (S2(5)).

1, 15, 255, 5175, 123795, 3427515, 108046575, 3824996175, 150346471275, 6499426608675, 306553491419175, 15668768604864375, 862827112324051875, 50929793720847916875, 3208139019437586609375, 214817175616326677769375, 15237402314816854944646875

Offset: 0

Author

Wolfdieter Lang, Oct 17 2008, Dec 04 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..360

Crossrefs

First column: A007696 (4-factorials). Third column A143169.

Programs

Mathematica

FullSimplify@Table[(-4)^n(8Sqrt[Pi]/Gamma[-3/2-n]-5Gamma[-5/4]/Gamma[-5/4-n]),{n, 0, 20}] (* Benedict W. J. Irwin, Apr 06 2017 *)

PARI

x='x+O('x^50); Vec(serlaplace((6 - 5*(1-4*x)^(1/4))/(1 -4*x)^(5/2))) \\ G. C. Greubel, May 25 2017

Formula

a(n) = A049029(n+2,2),n>=0.

E.g.f. with offset n=2: ((-1+(1-4*x)^(-1/4))^2)/2!.

E.g.f.: (6 - 5*(1-4*x)^(1/4))/(1-4*x)^(5/2) (offset n=0).

a(n) = (-4)^n*(8*Sqrt(Pi)/Gamma(-3/2-n)-5*Gamma(-5/4)/Gamma(-5/4-n)). - Benedict W. J. Irwin, Apr 06 2017