This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368530 #17 Dec 29 2023 08:05:19
%S A368530 0,1,12,75,364,1581,6540,26503,106524,426825,1708300,6834531,27339852,
%T A368530 109361605,437449164,1749800031,6999204220,27996821793,111987293004,
%U A368530 447949178875,1791796723500,7167186903261,28668747623692,114674990506935,458699962041564
%N A368530 a(n) = Sum_{k=1..n} k^3 * 4^(n-k).
%H A368530 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,28,-17,4).
%F A368530 G.f.: x * (1+4*x+x^2)/((1-4*x) * (1-x)^4).
%F A368530 a(n) = 8*a(n-1) - 22*a(n-2) + 28*a(n-3) - 17*a(n-4) + 4*a(n-5).
%F A368530 a(n) = (11*4^(n+1) - (9*n^3 + 36*n^2 + 60*n + 44))/27.
%F A368530 a(0) = 0; a(n) = 4*a(n-1) + n^3.
%o A368530 (PARI) a(n) = sum(k=1, n, k^3*4^(n-k));
%Y A368530 Cf. A000578, A000537, A213575, A066999.
%Y A368530 Cf. A097788, A368525.
%Y A368530 Cf. A014825, A368529.
%K A368530 nonn,easy
%O A368530 0,3
%A A368530 _Seiichi Manyama_, Dec 29 2023