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 A381386 #17 Feb 24 2025 08:09:17
%S A381386 1,1,6,73,1360,34321,1095584,42350673,1923628032,100430070721,
%T A381386 5926517800192,390116250605401,28341322114027520,2252512575040254801,
%U A381386 194421212092585943040,18110799663166635386017,1810994441189833169698816,193488658627430346315888385,21997611392941496027173879808
%N A381386 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^2) ).
%F A381386 a(n) = Sum_{k=0..n} k! * binomial(2*n+k+1,k)/(2*n+k+1) * A136630(n,k).
%F A381386 E.g.f.: ( (1/x) * Series_Reversion( x*(1 - sinh(x))^2 ) )^(1/2).
%o A381386 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381386 a(n) = sum(k=0, n, k!*binomial(2*n+k+1, k)/(2*n+k+1)*a136630(n, k));
%Y A381386 Cf. A136630, A381387.
%K A381386 nonn
%O A381386 0,3
%A A381386 _Seiichi Manyama_, Feb 22 2025