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 A372165 #10 Apr 21 2024 11:48:35
%S A372165 1,2,28,758,31160,1730562,121434364,10312487054,1028675082960,
%T A372165 117917384790914,15275849114906804,2207219937751153998,
%U A372165 351952462602081499480,61392924661901606654402,11629541557015551899838252,2377438129669444985664704078,521710054052646408966825988256
%N A372165 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(5/2) / (1 - x * A(x)) ).
%F A372165 E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A372183.
%F A372165 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 A372165 (PARI) a(n, r=2, s=1, t=5, 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 A372165 Cf. A371581, A372164, A372183.
%K A372165 nonn
%O A372165 0,2
%A A372165 _Seiichi Manyama_, Apr 21 2024