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 A096307 E.g.f.: exp(x)/(1-x)^6. 6

%I

%S 1,7,55,481,4645,49171,566827,7073725,95064361,1369375615,21054430591,

%T 344231563897,5964569413645,109196040092491,2106381399472435,

%U 42705264827626261,907920105215691217,20198878182718877815

%N E.g.f.: exp(x)/(1-x)^6.

%C Sum_{k = 0..n} A094816(n,k)*x^k give A000522(n), A001339(n), A082030(n), A095000(n), A095177(n) for x = 1, 2, 3, 4, 5 respectively.

%H G. C. Greubel, <a href="/A096307/b096307.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = Sum_{k = 0..n} A094916(n, k)*6^k.

%F a(n) = Sum_{k = 0..n} binomial(n, k)*(k+5)!/5!.

%F a(n) = 2F0(6,-n;;-1). - _Benedict W. J. Irwin_, May 27 2016

%t Table[HypergeometricPFQ[{6, -n}, {}, -1], {n, 0, 20}] (* _Benedict W. J. Irwin_, May 27 2016 *)

%t With[{nn = 250}, CoefficientList[Series[Exp[x]/(1 - x)^6, {x, 0, nn}], x] Range[0, nn]!] (* _G. C. Greubel_, May 27 2016 *)

%K nonn

%O 0,2

%A _Philippe DelĂ©ham_, Jun 26 2004

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)