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 A379456 #17 Feb 05 2025 09:22:39
%S A379456 1,2,13,151,2573,58221,1648345,56138461,2236816825,102135829609,
%T A379456 5259937376141,301678137203433,19072415186892325,1317869007328182349,
%U A379456 98818139178323981473,7991908824553634264101,693473520767940388417265,64266613784795934251538513
%N A379456 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + x*exp(x)) ).
%F A379456 a(n) = (n!/(n+1)) * Sum_{k=0..n} (2*n-k+1)^k * binomial(n+1,n-k)/k!.
%F A379456 E.g.f. A(x) satisfies A(x) = exp(x*A(x)) / ( 1 - x*exp(2*x*A(x)) ). - _Seiichi Manyama_, Feb 04 2025
%o A379456 (PARI) a(n) = n!*sum(k=0, n, (2*n-k+1)^k*binomial(n+1, n-k)/k!)/(n+1);
%Y A379456 Cf. A088690, A379846, A379847.
%Y A379456 Cf. A108919, A161633.
%Y A379456 Cf. A379699, A379700.
%K A379456 nonn
%O A379456 0,2
%A A379456 _Seiichi Manyama_, Dec 30 2024