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%I #8 Dec 25 2021 02:45:56
%S 0,1,18,132,680,2880,10752,36736,117504,357120,1041920,2939904,
%T 8067072,21618688,56770560,146472960,372113408,932511744,2308571136,
%U 5653135360,13707509760,32942063616,78525759488,185799278592,436627046400
%N a(n) = 2^(n-4)*n*(n+1)*(n^2+5*n-2).
%C Binomial transform of A000583.
%D A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,80,-80,32).
%F a(n) = Sum_{i=1..n} i^4 * binomial(n, i).
%F G.f.: x*(8*x^2-8*x-1)/(2*x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009
%F a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5). - _Wesley Ivan Hurt_, Dec 24 2021
%t LinearRecurrence[{10, -40, 80, -80, 32}, {0, 1, 18, 132, 680}, 30] (* _Wesley Ivan Hurt_, Dec 24 2021 *)
%Y Cf. A000583.
%K nonn,easy
%O 0,3
%A Yong Kong (ykong(AT)curagen.com), Dec 26 2000
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