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 A381449 #10 Feb 24 2025 05:41:16
%S A381449 1,2,10,90,1224,22450,517920,14395514,468414464,17474840226,
%T A381449 735559614720,34491849224602,1783268816102400,100786369113730898,
%U A381449 6182264844496971776,409065938149354422330,29043282491002728284160,2202461172795524123296834,177675452451923238962528256
%N A381449 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x * cosh(x))^2 ).
%C A381449 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381449 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381449 E.g.f. A(x) satisfies A(x) = (1 + x*A(x) * cosh(x*A(x)))^2.
%F A381449 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381447.
%F A381449 a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(2*n+2,k) * A185951(n,k).
%o A381449 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381449 a(n) = sum(k=0, n, k!*binomial(2*n+2, k)*a185951(n, k))/(n+1);
%Y A381449 Cf. A381171, A381450.
%Y A381449 Cf. A185951, A381447.
%K A381449 nonn
%O A381449 0,2
%A A381449 _Seiichi Manyama_, Feb 23 2025