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 A372179 #10 Apr 21 2024 11:40:56
%S A372179 1,2,12,134,2232,49762,1394236,47117982,1866217296,84810000194,
%T A372179 4350808646964,248736339576958,15682868019616408,1081153176108929250,
%U A372179 80906410246285190508,6531880775140905838238,565912845564569155284384,52373575389612727174282882
%N A372179 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) / (1 - x * A(x)) ).
%F A372179 E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A365012.
%F A372179 If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.
%o A372179 (PARI) a(n, r=2, s=1, t=1, u=2) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
%Y A372179 Cf. A365012, A372165, A372178.
%K A372179 nonn
%O A372179 0,2
%A A372179 _Seiichi Manyama_, Apr 21 2024