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%I #16 Jul 27 2021 21:21:28
%S 1,8,71,694,7421,86276,1084483,14665106,212385209,3280842496,
%T 53862855551,936722974958,17205245113141,332864226563324,
%U 6766480571358971,144202473398010826,3215159679583864433
%N E.g.f.: exp(x)/(1-x)^7.
%C Sum_{k=0..n} A094816(n,k)*x^k give A000522(n), A001339(n), A082030(n), A095000(n), A095177(n), A096307(n) for x = 1, 2, 3, 4, 5, 6 respectively.
%H G. C. Greubel, <a href="/A096341/b096341.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = Sum_{k = 0..n} A094816(n, k)*7^k.
%F a(n) = Sum_{k = 0..n} binomial(n, k)*(k+6)!/6!.
%F a(n) = 2F0(7,-n;;-1). - _Benedict W. J. Irwin_, May 27 2016
%F From _Peter Bala_, Jul 26 2021: (Start)
%F a(n) = (n+7)*a(n-1) - (n-1)*a(n-2) with a(0) = 1 and a(1) = 8.
%F First-order recurrence: P(n-1)*a(n) = n*P(n)*a(n-1) + 1 with a(0) = 1, where P(n) = n^6 + 15*n^5 + 100*n^4 + 355*n^3 + 694*n^2 + 689*n + 265 = A094795(n).
%F (End)
%t Table[HypergeometricPFQ[{7, -n}, {}, -1], {n, 0, 20}] (* _Benedict W. J. Irwin_, May 27 2016 *)
%t With[{nn = 250}, CoefficientList[Series[Exp[x]/(1 - x)^7, {x, 0, nn}], x] Range[0, nn]!] (* _G. C. Greubel_, May 27 2016 *)
%Y Cf. E.g.f. exp(x)/(1-x)^k: A000522 (k = 1), A001339 (k = 2), A082030 (k = 3), A095000 (k = 4), A095177 (k = 5), A096307 (k = 6).
%Y Cf. A094795, A094816.
%K nonn
%O 0,2
%A _Philippe Deléham_, Jun 28 2004
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