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 A381387 #16 Feb 24 2025 08:09:04
%S A381387 1,2,14,182,3520,91002,2954400,115638014,5303063552,278979672050,
%T A381387 16565016146176,1095997724407302,79966475806040064,
%U A381387 6379010456725968362,552344502268240535552,51595059327775839277646,5171865567269556457308160,553764742712510134123863522
%N A381387 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)) )^2.
%F A381387 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381386.
%F A381387 a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n+k+2,k)/(2*n+k+2) * A136630(n,k).
%F A381387 E.g.f.: (1/x) * Series_Reversion( x*(1 - sinh(x))^2 ).
%o A381387 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381387 a(n) = 2*sum(k=0, n, k!*binomial(2*n+k+2, k)/(2*n+k+2)*a136630(n, k));
%Y A381387 Cf. A136630, A381386.
%K A381387 nonn
%O A381387 0,2
%A A381387 _Seiichi Manyama_, Feb 22 2025