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 A386365 #15 Jul 21 2025 06:38:19
%S A386365 1,1,8,118,2536,71600,2504320,104482000,5063797760,279579704320,
%T A386365 17322126976000,1190107376057600,89795437443712000,
%U A386365 7381088691027251200,656522501105485414400,62825541269686074880000,6436003096247592964096000,702751431134395346063360000
%N A386365 Expansion of e.g.f. (Sum_{k>=0} binomial(3*k,k) * x^k)^(1/3).
%F A386365 a(n) ~ Pi * 3^(3*n - 1/3) * n^(n - 1/3) / (Gamma(1/3)^2 * exp(n) * 2^(2*n - 1/2)). - _Vaclav Kotesovec_, Jul 19 2025
%F A386365 E.g.f.: B(x)^(1/3) where B(x) is the g.f. of A005809. - _Georg Fischer_, Jul 21 2025
%t A386365 nmax = 20; CoefficientList[Series[Sum[Binomial[3*k,k] * x^k, {k, 0, nmax}]^(1/3), {x, 0, nmax}], x] * Range[0,nmax]! (* _Vaclav Kotesovec_, Jul 19 2025 *)
%o A386365 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(3*k, k)*x^k)^(1/3)))
%Y A386365 Cf. A000142, A007696, A005809, A386366.
%Y A386365 Cf. A378483.
%K A386365 nonn
%O A386365 0,3
%A A386365 _Seiichi Manyama_, Jul 19 2025