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 A382449 #32 Apr 13 2025 03:25:29
%S A382449 1,1,7,64,745,10576,177121,3414622,74389729,1805424040,48264466321,
%T A382449 1408241206186,44508262018177,1514115583435924,55142123112150985,
%U A382449 2139885098048098486,88128888655032851521,3838126991973342097072,176206944426651875454049
%N A382449 Expansion of e.g.f. exp( x/(1-2*x)^(3/2) ).
%F A382449 a(n) = n! * Sum_{k=0..n} 2^(n-k) * binomial(n+k/2-1,n-k)/k!.
%F A382449 a(n) ~ 3^(1/5) * 2^(n + 1/10) * exp(-3^(-1/5)*2^(-13/5)*n^(1/5) + 5*3^(-3/5)*2^(-4/5)*n^(3/5) - n) * n^(n - 1/5) / sqrt(5). - _Vaclav Kotesovec_, Apr 13 2025
%t A382449 nmax = 20; CoefficientList[Series[E^(x/(1 - 2*x)^(3/2)), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Apr 13 2025 *)
%o A382449 (PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*binomial(n+k/2-1, n-k)/k!);
%Y A382449 Cf. A001879, A362204.
%K A382449 nonn,easy
%O A382449 0,3
%A A382449 _Seiichi Manyama_, Apr 03 2025