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

0,2

Links

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

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A218634 A218238 A015691 * A027775 A334995 A099273

Adjacent sequences: A145559 A145560 A145561 * A145563 A145564 A145565

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 17 2008, Dec 04 2008

Status

approved