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 A385305 #12 Jun 28 2025 03:10:53
%S A385305 1,1,4,29,296,3921,63904,1236509,27700096,705098241,20100847104,
%T A385305 634406699389,21959759364096,827184049670161,33684401687855104,
%U A385305 1474548883501060669,69051807696652599296,3444499079760040247681,182339939994632235515904,10209271857672376613472349
%N A385305 Expansion of e.g.f. 1/(1 - 3 * sinh(x))^(1/3).
%F A385305 a(n) = Sum_{k=0..n} A007559(k) * A136630(n,k).
%F A385305 a(n) ~ sqrt(Pi) * 2^(1/3) * n^(n - 1/6) / (5^(1/6) * Gamma(1/3) * exp(n) * log((1 + sqrt(10))/3)^(n + 1/3)). - _Vaclav Kotesovec_, Jun 28 2025
%o A385305 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A385305 a007559(n) = prod(k=0, n-1, 3*k+1);
%o A385305 a(n) = sum(k=0, n, a007559(k)*a136630(n, k));
%Y A385305 Cf. A006154, A385304.
%Y A385305 Cf. A380017, A385307, A385309, A385311.
%Y A385305 Cf. A007559, A136630, A235135.
%K A385305 nonn
%O A385305 0,3
%A A385305 _Seiichi Manyama_, Jun 24 2025