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 A380718 #10 Jan 31 2025 09:25:00 %S A380718 1,2,17,277,6809,225381,9408745,474835159,28128322801,1913917635433, %T A380718 147124118481641,12610993501595523,1192699876840875529, %U A380718 123380247466574450509,13858619936380747514953,1679795510876270598645631,218541202774350975212752865,30376105717226232363041309265 %N A380718 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x*A(x)). %F A380718 a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(2*n,n-k)/k!. %o A380718 (PARI) a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(2*n, n-k)/k!); %Y A380718 Cf. A380663, A380719. %Y A380718 Cf. A377831. %K A380718 nonn %O A380718 0,2 %A A380718 _Seiichi Manyama_, Jan 30 2025