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%I #23 Sep 08 2022 08:46:17
%S 0,1,31,196,756,2226,5502,12012,23892,44187,77077,128128,204568,
%T 315588,472668,689928,984504,1376949,1891659,2557324,3407404,4480630,
%U 5821530,7480980,9516780,11994255,14986881,18576936,22856176,27926536,33900856,40903632,49071792
%N a(n) = 25*binomial(n-1,6) + binomial(n-1,5).
%H Vincenzo Librandi, <a href="/A274501/b274501.txt">Table of n, a(n) for n = 5..1000</a>
%H Q. T. Bach, R. Paudyal, J. B. Remmel, <a href="http://arxiv.org/abs/1510.04310">A Fibonacci analogue of Stirling numbers</a>, arXiv preprint arXiv:1510.04310 [math.CO], 2015 (page 25).
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: x^6*(1 + 24*x)/(1-x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F a(n) = (n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(25*n-144)/720. - _Wesley Ivan Hurt_, Jun 25 2016
%p A274501:=n->25*binomial(n-1,6) + binomial(n-1,5): seq(A274501(n), n=5..50); # _Wesley Ivan Hurt_, Jun 25 2016
%t Table[25 Binomial[n - 1, 6] + Binomial[n - 1, 5], {n, 5, 40}]
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,31,196,756,2226,5502},40] (* _Harvey P. Dale_, Mar 09 2022 *)
%o (Magma) [25*Binomial(n-1,6)+Binomial(n-1,5): n in [5..40]];
%o (PARI) concat(0, Vec(x^6*(1+24*x)/(1-x)^7 + O(x^99))) \\ _Altug Alkan_, Jun 27 2016
%Y Cf. A253945.
%K nonn,easy
%O 5,3
%A _Vincenzo Librandi_, Jun 25 2016
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