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 A381303 #7 Feb 20 2025 08:39:35
%S A381303 1,1,0,1,4,1,32,183,192,4921,33664,88573,2100224,16487745,83890176,
%T A381303 1920800731,17243373568,143156073841,3236025171968,33490813489497,
%U A381303 401094916964352,9092346624868321,109434837281013760,1724106500663768191,39706910863092875264
%N A381303 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^(1/2)) / A(x)^(3/2) ).
%F A381303 a(n) = Sum_{k=0..n} k! * binomial(n/2-k/2+1,k)/(n/2-k/2+1) * A136630(n,k).
%o A381303 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381303 a(n) = sum(k=0, n, k!*binomial(n/2-k/2+1, k)/(n/2-k/2+1)*a136630(n, k));
%Y A381303 Cf. A136630.
%K A381303 nonn
%O A381303 0,5
%A A381303 _Seiichi Manyama_, Feb 19 2025