A095740 - OEIS

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

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OFFSET

0,2

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

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

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 *)

CROSSREFS

Sequence in context: A199760 A082181 A190919 * A075508 A095176 A061749

Adjacent sequences: A095737 A095738 A095739 * A095741 A095742 A095743

KEYWORD

nonn

AUTHOR

Philippe Deléham Jul 09 2004

STATUS

approved