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 A355220 #7 Jun 26 2022 04:21:13
%S A355220 1,7,81,1399,32289,931687,32259441,1303134679,60160827969,
%T A355220 3124574220487,180312309395601,11445969681199159,792626097462398049,
%U A355220 59462922484586318887,4804064349575887075761,415847988794676360818839,38396277196654611908582529,3766800071614388562865514887
%N A355220 a(n) = Sum_{k>=1} (4*k - 1)^n / 2^k.
%F A355220 E.g.f.: exp(3*x) / (2 - exp(4*x)).
%F A355220 a(0) = 1; a(n) = 3^n + Sum_{k=1..n} binomial(n,k) * 4^k * a(n-k).
%F A355220 a(n) = Sum_{k=0..n} binomial(n,k) * 3^(n-k) * 4^k * A000670(k).
%F A355220 a(n) ~ n! * 2^(2*n - 1/4) / log(2)^(n+1). - _Vaclav Kotesovec_, Jun 24 2022
%t A355220 nmax = 17; CoefficientList[Series[Exp[3 x]/(2 - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A355220 a[0] = 1; a[n_] := a[n] = 3^n + Sum[Binomial[n, k] 4^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]
%Y A355220 Cf. A000629, A000670, A080253, A259533, A285067, A328183, A355218, A355219.
%K A355220 nonn
%O A355220 0,2
%A A355220 _Ilya Gutkovskiy_, Jun 24 2022