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 A381412 #10 Feb 23 2025 08:08:47
%S A381412 1,2,4,10,64,754,9024,109050,1544960,27480162,567449600,12641553258,
%T A381412 303021248512,7982668175954,231306526932992,7245659221444186,
%U A381412 242226980924424192,8623216994933650114,327015684198600278016,13169904418920596839626,560434137147666884198400
%N A381412 E.g.f. A(x) satisfies A(x) = exp( 2 * sinh(x * A(x)) / A(x) ).
%F A381412 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381411.
%F A381412 a(n) = 2 * Sum_{k=0..n} (2*n-2*k+2)^(k-1) * A136630(n,k).
%o A381412 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381412 a(n) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*a136630(n, k));
%Y A381412 Cf. A136630, A381411.
%K A381412 nonn
%O A381412 0,2
%A A381412 _Seiichi Manyama_, Feb 23 2025