A111778 Fifth column (m=4) of unsigned triangle A111595.

1, 20, 315, 4620, 67830, 1020600, 15961050, 260706600, 4461170175, 80002622700, 1503527550525, 29583578524500, 608837350621500, 13088359506222000, 293538127312930500, 6858722586405690000, 166752692881988338125

Offset

4,2

Links

Table of n, a(n) for n=4..20.

Formula

E.g.f. (1/sqrt(1-x^2))*((x/(1-x))^4)/4!.

a(n)=(n!/4!)*sum(binomial(2*k, k)*binomial(n-2*k-1, 3)/(4^k), k=0..floor((n-4)/2)), n>=4.

Conjecture: (-n+4)*a(n) +4*n*a(n-1) +n*(n-1)^2*a(n-2)=0. - R. J. Mathar, Jun 08 2016

Mathematica

With[{nn=30}, Drop[CoefficientList[Series[1/Sqrt[1-x^2] (x/(1-x))^4/4!, {x, 0, nn}], x] Range[0, nn]!, 4]] (* Harvey P. Dale, Apr 05 2015 *)

Crossrefs

Sequence in context: A034094 A011197 A054621 * A024387 A307173 A101310

Adjacent sequences: A111775 A111776 A111777 * A111779 A111780 A111781

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 23 2005

Status

approved