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 A385304 #15 Jun 28 2025 03:05:26
%S A385304 1,1,3,16,117,1096,12543,169576,2644617,46735936,922993083,
%T A385304 20145579136,481555537917,12511452674176,351058439096823,
%U A385304 10579734482269696,340820224678288017,11687491783287586816,425075150516293691763,16343274366458168160256,662325275389743380902917
%N A385304 Expansion of e.g.f. 1/(1 - 2 * sinh(x))^(1/2).
%F A385304 a(n) = Sum_{k=0..n} A001147(k) * A136630(n,k).
%F A385304 a(n) ~ sqrt(2) * n^n / (5^(1/4) * exp(n) * log((1 + sqrt(5))/2)^(n + 1/2)). - _Vaclav Kotesovec_, Jun 28 2025
%o A385304 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A385304 a001147(n) = prod(k=0, n-1, 2*k+1);
%o A385304 a(n) = sum(k=0, n, a001147(k)*a136630(n, k));
%Y A385304 Cf. A006154, A385305.
%Y A385304 Cf. A380015, A385306, A385308, A385310.
%Y A385304 Cf. A001147, A136630, A235134, A364822.
%K A385304 nonn
%O A385304 0,3
%A A385304 _Seiichi Manyama_, Jun 24 2025