A095740 E.g.f.: exp(x)/(1-x)^9.

1, 10, 109, 1288, 16417, 224686, 3288205, 51263164, 848456353, 14862109042, 274743964621, 5346258202000, 109249238631169, 2339328151461718, 52384307381414317, 1224472783033479556, 29826054965115774145

Offset: 0

Author

Philippe Deléham Jul 09 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), A095722(n) for x = 1, 2, 3, 4, 5, 6, 7, 8.

Links

• Robert Israel, Table of n, a(n) for n = 0..440

Programs

Maple

seq(simplify(hypergeom([9,-n],[],-1)),n=0..30); # Robert Israel, May 27 2016

Mathematica

Table[HypergeometricPFQ[{9, -n}, {}, -1], {n, 0, 20}] (* Benedict W. J. Irwin, May 27 2016 *)

Formula

a(n) = Sum_{k = 0..n} A094816(n, k)*9^k.

a(n) = Sum_{k = 0..n} binomial(n, k)*(k+8)!/8!.

a(n) = 2F0(9,-n;;-1). - Benedict W. J. Irwin, May 27 2016

a(n) = ((n^8 + 28*n^7 + 350*n^6 + 2492*n^5 + 10899*n^4 + 29596*n^3 + 48082*n^2 + 42048*n + 14833) * Gamma(n+1,1)*e + n^7 + 28*n^6 + 349*n^5 + 2465*n^4 + 10579*n^3 + 27501*n^2 + 40132*n + 25487) / 40320. - Robert Israel, May 27 2016