A111782 Ninth column (m=8) of unsigned triangle A111595.

1, 72, 3285, 122760, 4138695, 132046200, 4096887795, 125691766200, 3854667766950, 119027264756400, 3719190784859550, 118004440103550000, 3811105656937829250, 125500234402721178000, 4218813452749267622250

Offset: 8

Author

Wolfdieter Lang, Aug 23 2005

Keywords

• nonn
• easy

Programs

Mathematica

Drop[With[{nn=30},CoefficientList[Series[1/Sqrt[1-x^2] (x/(1-x))^8/8!,{x,0,nn}],x] Range[ 0,nn]!],8] (* Harvey P. Dale, Nov 17 2022 *)

Formula

E.g.f. (1/sqrt(1-x^2))*((x/(1-x))^8)/8!.

a(n)=(n!/8!)*sum(binomial(2*k, k)*binomial(n-2*k-1, 7)/(4^k), k=0..floor((n-8)/2)), n>=8.