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 A293565 #28 Jun 09 2024 00:14:48
%S A293565 1,-1,1,-1,-23,119,-359,-4201,58801,-359857,-2121839,74851919,
%T A293565 -784376999,-1072414201,192596540137,-3167640042841,9241215940321,
%U A293565 860635956717599,-21290802661288799,157132294452113183,5980504635868174921,-220612220726623344361
%N A293565 Expansion of e.g.f. Product_{k>=0} exp(-x^(3*k+1)).
%H A293565 Seiichi Manyama, <a href="/A293565/b293565.txt">Table of n, a(n) for n = 0..447</a>
%F A293565 E.g.f.: exp(x/(x^3 - 1)).
%F A293565 a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * (3*k+1)! * a(n-3*k-1). - _Ilya Gutkovskiy_, Feb 24 2022
%F A293565 a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^(n-k) * binomial(n-2*k-1,k)/(n-3*k)!. - _Seiichi Manyama_, Jun 08 2024
%t A293565 CoefficientList[Series[E^(x/(x^3 - 1)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 13 2017 *)
%o A293565 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(x^3-1))))
%o A293565 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(1/prod(m=0, N, exp(x^(3*m+1)))))
%Y A293565 E.g.f.: Product_{m>=0} exp(-x^(k*m+1)): A293116 (k=1), A293532 (k=2), this sequence (k=3), A293566 (k=4).
%Y A293565 Cf. A293493.
%K A293565 sign
%O A293565 0,5
%A A293565 _Seiichi Manyama_, Oct 12 2017