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 A381478 #12 Feb 25 2025 01:58:01
%S A381478 1,2,14,186,3696,98290,3283920,132311354,6246905728,338374946466,
%T A381478 20688891816960,1409607482926522,105914955915952128,
%U A381478 8701156803022552466,775923181679913938944,74646655589398509637050,7706371729268071660093440,849834260414107910987980354
%N A381478 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cosh(x * A(x)) )^2.
%C A381478 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381478 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381477.
%F A381478 a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n+k+2,k)/(2*n+k+2) * A185951(n,k).
%F A381478 E.g.f.: (1/x) * Series_Reversion( x*(1 - x*cosh(x))^2 ).
%o A381478 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381478 a(n) = 2*sum(k=0, n, k!*binomial(2*n+k+2, k)/(2*n+k+2)*a185951(n, k));
%Y A381478 Cf. A185951, A377546, A381387, A381449, A381477.
%K A381478 nonn
%O A381478 0,2
%A A381478 _Seiichi Manyama_, Feb 24 2025