%I #17 May 29 2016 08:16:06
%S 1,10,109,1288,16417,224686,3288205,51263164,848456353,14862109042,
%T 274743964621,5346258202000,109249238631169,2339328151461718,
%U 52384307381414317,1224472783033479556,29826054965115774145
%N E.g.f.: exp(x)/(1-x)^9.
%C 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.
%H Robert Israel, <a href="/A095740/b095740.txt">Table of n, a(n) for n = 0..440</a>
%F a(n) = Sum_{k = 0..n} A094816(n, k)*9^k.
%F a(n) = Sum_{k = 0..n} binomial(n, k)*(k+8)!/8!.
%F a(n) = 2F0(9,-n;;-1). - _Benedict W. J. Irwin_, May 27 2016
%F 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
%p seq(simplify(hypergeom([9,-n],[],-1)),n=0..30); # _Robert Israel_, May 27 2016
%t Table[HypergeometricPFQ[{9, -n}, {}, -1], {n, 0, 20}] (* _Benedict W. J. Irwin_, May 27 2016 *)
%K nonn
%O 0,2
%A _Philippe Deléham_ Jul 09 2004