A095722 E.g.f.: exp(x)/(1-x)^8.

1, 9, 89, 961, 11265, 142601, 1940089, 28245729, 438351041, 7226001865, 126122874201, 2324074591169, 45094140207169, 919088049256521, 19633713260950265, 438708172312264801, 10234490436580101249

Offset: 0

Author

Philippe Deléham, Jul 08 2004

Keywords

• nonn

Comments

Sum_{k = 0..n} A094816(n,k)*x^k gives A000522(n), A001339(n), A082030(n), A095000(n), A095177(n), A096307(n), A096341(n) for x = 1, 2, 3, 4, 5, 6, 7 respectively.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[x]/(1-x)^8,{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, May 26 2013 *)
Table[HypergeometricPFQ[{8, -n}, {}, -1], {n, 0, 20}] (* Benedict W. J. Irwin, May 27 2016 *)

Formula

a(n) = Sum_{k = 0..n} A094816(n, k)*8^k.

a(n) = Sum_{k = 0..n} binomial(n, k)*(k+7)! / 7!.

a(n) = 2F0(8,-n;;-1). - Benedict W. J. Irwin, May 27 2016