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 A382652 #24 Apr 19 2025 05:44:17
%S A382652 1,1,11,151,2601,54401,1341571,38115351,1225252561,43935295681,
%T A382652 1737463744251,75075845199191,3517448555579641,177538212306653121,
%U A382652 9600694935999031411,553606933661659742551,33899768045328467219361,2196417680635853609034881,150094038119761737476004331
%N A382652 Expansion of e.g.f. exp( x/(1-3*x)^(5/3) ).
%F A382652 a(n) = n! * Sum_{k=0..n} 3^(n-k) * binomial(n+2*k/3-1,n-k)/k!.
%F A382652 a(n) ~ 2^(-3/2) * 5^(3/16) * 3^(n + 1/8) * n^(n - 3/16) * exp(-3^(-3/2)*5^(-1/4)*n^(1/4)/2 + 8*5^(-5/8)*3^(-3/4)*n^(5/8) - n). - _Vaclav Kotesovec_, Apr 19 2025
%p A382652 exp(x/(1-3*x)^(5/3)) ;
%p A382652 taylor(%,x=0,60) ;
%p A382652 L := gfun[seriestolist](%) ;
%p A382652 seq( op(i,L)*(i-1)!,i=1..nops(L)) ; # _R. J. Mathar_, Apr 08 2025
%o A382652 (PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*binomial(n+2*k/3-1, n-k)/k!);
%Y A382652 Cf. A362188, A362205, A382643.
%K A382652 nonn,easy
%O A382652 0,3
%A A382652 _Seiichi Manyama_, Apr 03 2025