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 A381408 #8 Feb 23 2025 08:02:20
%S A381408 1,2,4,14,160,2202,28384,419302,8238080,193340978,4860711424,
%T A381408 132391420350,4045976651776,137295166640842,5028417873133568,
%U A381408 197042617602645398,8292209178735935488,374117497443421923426,17958577129581151387648,912189896002576287703918
%N A381408 E.g.f. A(x) satisfies A(x) = exp( 2 * x * cosh(x * A(x)) ).
%C A381408 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381408 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381407.
%F A381408 a(n) = 2 * Sum_{k=0..n} (2*n-2*k+2)^(k-1) * A185951(n,k).
%o A381408 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381408 a(n) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*a185951(n, k));
%Y A381408 Cf. A185951, A381407.
%K A381408 nonn
%O A381408 0,2
%A A381408 _Seiichi Manyama_, Feb 23 2025