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 A384351 #11 May 29 2025 07:03:08
%S A384351 1,1,7,143,6140,455828,51947988,8414718996,1836791273514,
%T A384351 519582028795210,184852108308617398,80776494267416227078,
%U A384351 42529172631705836804876,26553065315757661351020284,19397441882229095276127402500,16390942374821715002096327774628
%N A384351 Expansion of Product_{k>=1} 1/(1 - k*(k+1)/2 * x)^((1/2)^(k+2)).
%F A384351 G.f.: exp(Sum_{k>=1} A055203(k) * x^k/k).
%F A384351 a(n) ~ sqrt(Pi) * 2^(n - 1/2) * n^(2*n - 1/2) / (exp(2*n) * log(2)^(2*n+1)). - _Vaclav Kotesovec_, May 29 2025
%t A384351 nmax = 20; CoefficientList[Series[Exp[Sum[Sum[Sum[(-1)^j*Binomial[i, j]*((i - j)*(i - j - 1)/2)^k, {j, 0, i}], {i, 0, 2 k}]*x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 29 2025 *)
%o A384351 (PARI) a262809(n, k) = sum(i=0, k*n, sum(j=0, i, (-1)^j*binomial(i, j)*binomial(i-j, n)^k));
%o A384351 my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a262809(2, k)*x^k/k)))
%Y A384351 Cf. A084784, A384352, A384353.
%Y A384351 Cf. A055203, A262809.
%K A384351 nonn
%O A384351 0,3
%A A384351 _Seiichi Manyama_, May 27 2025