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 A355421 #17 Jul 02 2022 10:07:35
%S A355421 1,6,50,504,5870,76872,1111646,17522664,298133054,5433157512,
%T A355421 105396184478,2165189912040,46901678992958,1067332196912136,
%U A355421 25435754924426270,633014456504059368,16411191933603611198,442258823578968351624
%N A355421 Expansion of e.g.f. exp(Sum_{k=1..3} (exp(k*x) - 1)).
%F A355421 a(0) = 1; a(n) = Sum_{k=1..n} (1 + 2^k + 3^k) * binomial(n-1,k-1) * a(n-k).
%o A355421 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, 3, exp(k*x)-1))))
%o A355421 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (1+2^j+3^j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A355421 Column k=3 of A355423.
%Y A355421 Cf. A004701, A306027, A355379, A355380.
%K A355421 nonn
%O A355421 0,2
%A A355421 _Seiichi Manyama_, Jul 01 2022