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 A381447 #10 Feb 24 2025 05:39:11
%S A381447 1,1,4,33,432,7745,175680,4818457,155138816,5738752161,239890406400,
%T A381447 11184338164241,575437530083328,32387311520034913,1979498673768132608,
%U A381447 130566701113312750665,9244392468538216611840,699309477932976288024257,56289911059840766752456704
%N A381447 E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2 * cosh(x*A(x)^2).
%C A381447 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381447 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381447 E.g.f.: ( (1/x) * Series_Reversion( x/(1 + x * cosh(x))^2 ) )^(1/2).
%F A381447 a(n) = (1/(2*n+1)) * Sum_{k=0..n} k! * binomial(2*n+1,k) * A185951(n,k).
%o A381447 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381447 a(n) = sum(k=0, n, k!*binomial(2*n+1, k)*a185951(n, k))/(2*n+1);
%Y A381447 Cf. A381171, A381448.
%Y A381447 Cf. A185951.
%K A381447 nonn
%O A381447 0,3
%A A381447 _Seiichi Manyama_, Feb 23 2025