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 A381444 #9 Feb 24 2025 05:36:03
%S A381444 1,1,5,52,837,18276,504673,16871632,662646281,29912003344,
%T A381444 1526065495101,86843677613760,5454045493422925,374720831464254016,
%U A381444 27958655248431100313,2251304544037066606336,194594761915894781438481,17971382474574151984603392,1766073848394482007514748533
%N A381444 Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-2*x * cosh(x)) ) )^(1/2).
%C A381444 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381444 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381444 E.g.f. A(x) satisfies A(x) = exp( x * A(x)^2 * cosh(x * A(x)^2) ).
%F A381444 a(n) = Sum_{k=0..n} (2*n+1)^(k-1) * A185951(n,k).
%o A381444 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381444 a(n) = sum(k=0, n, (2*n+1)^(k-1)*a185951(n, k));
%Y A381444 Cf. A185951, A381143.
%K A381444 nonn
%O A381444 0,3
%A A381444 _Seiichi Manyama_, Feb 23 2025