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 A343561 #29 Nov 13 2021 10:21:28
%S A343561 4,12,33,86,216,528,1264,2976,6912,15872,36096,81408,182272,405504,
%T A343561 897024,1974272,4325376,9437184,20512768,44433408,95944704,206569472,
%U A343561 443547648,950009856,2030043136,4328521728,9210691584,19562233856,41473277952,87778394112,185488900096
%N A343561 2nd row of A341867: a(n) = (n^2+15*n+32)*2^(n-3).
%H A343561 Jianing Song, <a href="/A343561/b343561.txt">Table of n, a(n) for n = 0..1000</a>
%H A343561 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A343561 a(n) = Sum_{k=0..n} binomial(n,k) * (k^2+7*k+8)/2.
%F A343561 G.f.: (2 - 3*x)^2/(1 - 2*x)^3.
%F A343561 E.g.f.: exp(2*x) * (x^2/2 + 4*x + 4).
%t A343561 a[n_] := (n^2 + 15*n + 32)*2^(n - 3); Array[a, 31, 0] (* _Amiram Eldar_, Nov 08 2021 *)
%o A343561 (PARI) a(n) = (n^2+15*n+32)*2^(n-3)
%Y A343561 Cf. A341867.
%K A343561 nonn,easy
%O A343561 0,1
%A A343561 _Jianing Song_, Nov 07 2021