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 A380755 #7 Feb 01 2025 08:42:20 %S A380755 1,2,25,622,23601,1211306,78585241,6171434550,569338685089, %T A380755 60362321078674,7232765564919321,966640735654507838, %U A380755 142570635491126076625,23003561321179411452858,4030628821337323603113241,762175215630679850520288646,154707566043362563540600474689 %N A380755 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 / (1 - x * A(x)^2)^2) / (1 - x * A(x)^2). %F A380755 a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(3*n+k,n-k)/k!. %o A380755 (PARI) a(n) = n!*sum(k=0, n, (2*n+1)^(k-1)*binomial(3*n+k, n-k)/k!); %Y A380755 Cf. A380723, A380726. %K A380755 nonn %O A380755 0,2 %A A380755 _Seiichi Manyama_, Feb 01 2025