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 A352357 #14 Mar 13 2022 13:37:17
%S A352357 1,1,6,40,364,4155,56836,907158,16547896,339587445,7743161740,
%T A352357 194212763756,5314051343932,157520046898695,5028409083962824,
%U A352357 171984217743856890,6274444932921616176,243215342466576246185,9982290554423689511124,432464578359391409082952
%N A352357 Expansion of e.g.f. 1/(1 - Sum_{k>=1} binomial(k+2,3) * x^k/k!).
%F A352357 E.g.f.: 1/(1 - (x + x^2 + x^3/6)*exp(x)).
%F A352357 a(0) = 1; a(n) = Sum_{k=1..n} binomial(k+2,3) * binomial(n,k) * a(n-k).
%o A352357 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-(x+x^2+x^3/6)*exp(x))))
%o A352357 (PARI) a(n) = if(n==0, 1, sum(k=1, n, binomial(k+2, 3)*binomial(n, k)*a(n-k)));
%Y A352357 Cf. A006153, A308946, A352358.
%Y A352357 Cf. A000292, A308862, A346889.
%K A352357 nonn
%O A352357 0,3
%A A352357 _Seiichi Manyama_, Mar 13 2022