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 A382643 #26 Apr 17 2025 03:53:22
%S A382643 1,1,9,109,1697,32401,733081,19167709,568351169,18833921857,
%T A382643 689436160361,27616959669421,1201138514382049,56349982190989969,
%U A382643 2835621797645900537,152321976433436677981,8697876904012444443521,526015632425455532060929,33581536744768011688139209
%N A382643 Expansion of e.g.f. exp( x/(1-3*x)^(4/3) ).
%F A382643 a(n) = n! * Sum_{k=0..n} 3^(n-k) * binomial(n+k/3-1,n-k)/k!.
%F A382643 a(n) ~ 2^(3/7) * 3^(n + 1/14) * n^(n - 3/14) * exp(-2^(-2/7)*3^(-12/7)*n^(1/7) + 7*2^(-8/7)*3^(-6/7)*n^(4/7) - n) / sqrt(7). - _Vaclav Kotesovec_, Apr 17 2025
%o A382643 (PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*binomial(n+k/3-1, n-k)/k!);
%Y A382643 Cf. A362188, A362205, A382652.
%K A382643 nonn,easy
%O A382643 0,3
%A A382643 _Seiichi Manyama_, Apr 03 2025