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A274503 a(n) = 301*binomial(n-1,8)+52*binomial(n-1,7)+binomial(n-1,6).

%I A274503 #17 Sep 08 2022 08:46:17
%S A274503 0,0,1,59,745,4665,19995,67287,191103,478335,1085370,2276560,4476758,
%T A274503 8340982,14844570,25397490,41986770,67351314,105193671,160433625,
%U A274503 239508775,350727575,504680605,714716145,997486425,1373571225,1868185800,2511980406,3341939004
%N A274503 a(n) = 301*binomial(n-1,8)+52*binomial(n-1,7)+binomial(n-1,6).
%H A274503 Vincenzo Librandi, <a href="/A274503/b274503.txt">Table of n, a(n) for n = 5..1000</a>
%H A274503 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 A274503 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A274503 G.f.: x^7*(1 + 50*x + 250*x^2)/(1-x)^9.
%F A274503 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).
%F A274503 a(n) = (n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(301*n^2-4099*n+14000)/40320. - _Wesley Ivan Hurt_, Jun 25 2016
%p A274503 A274503:=n->301*binomial(n-1,8)+52*binomial(n-1,7)+binomial(n-1,6): seq(A274503(n), n=5..50); # _Wesley Ivan Hurt_, Jun 25 2016
%t A274503 Table[301*Binomial[n-1,8]+52*Binomial[n-1,7]+Binomial[n-1,6], {n, 5, 40}]
%o A274503 (Magma) [301*Binomial(n-1,8)+52*Binomial(n-1,7)+Binomial(n-1,6): n in [5..40]];
%o A274503 (PARI) concat([0, 0], Vec(x^7*(1 + 50*x + 250*x^2)/(1-x)^9 + O(x^100))) \\ _Altug Alkan_, Jun 26 2016
%Y A274503 Cf. A253945, A274501, A274502.
%K A274503 nonn,easy
%O A274503 5,4
%A A274503 _Vincenzo Librandi_, Jun 25 2016