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 A328182 #9 Aug 09 2021 03:50:35
%S A328182 1,3,27,351,6075,131463,3413907,103429791,3581223435,139498558263,
%T A328182 6037616347587,287444492409231,14929010774254395,839982382565841063,
%U A328182 50897213545996785267,3304312091004451756671,228821504027595115886955,16836102104577636004291863,1311625494765417347634022947
%N A328182 Expansion of e.g.f. 1 / (2 - exp(3*x)).
%F A328182 a(0) = 1; a(n) = Sum_{k=1..n} 3^k * binomial(n,k) * a(n-k).
%F A328182 a(n) = Sum_{k>=0} (3*k)^n / 2^(k + 1).
%F A328182 a(n) = 3^n * A000670(n).
%F A328182 a(n) ~ n! * 3^n / (2 * log(2)^(n+1)). - _Vaclav Kotesovec_, Aug 09 2021
%p A328182 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A328182 a(n-j)*binomial(n, j)*3^j, j=1..n))
%p A328182 end:
%p A328182 seq(a(n), n=0..20); # _Alois P. Heinz_, Oct 06 2019
%t A328182 nmax = 18; CoefficientList[Series[1/(2 - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A328182 a[0] = 1; a[n_] := a[n] = Sum[3^k Binomial[n, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%t A328182 Table[3^n HurwitzLerchPhi[1/2, -n, 0]/2, {n, 0, 18}]
%Y A328182 Cf. A000670, A216794, A247452, A328183.
%K A328182 nonn
%O A328182 0,2
%A A328182 _Ilya Gutkovskiy_, Oct 06 2019