|
%I #19 Feb 26 2022 10:52:36
%S 1,1,1,1,1,121,721,2521,6721,378001,5473441,39972241,199679041,
%T 7005552841,176899522801,2186722497961,17454339826561,459473703430561,
%U 16503993702423361,306140370496394401,3555223271216311681,80917223353652470681,3568770455830785208081
%N E.g.f.: exp(x/(1 - x^4)).
%F E.g.f.: Product_{k>0} exp(x^(4*k-3)).
%F a(n) ~ exp(1/4 + sqrt(n) - n) * n^(n-1/4) / 2. - _Vaclav Kotesovec_, Oct 11 2017
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * (4*k+1)! * a(n-4*k-1). - _Ilya Gutkovskiy_, Feb 24 2022
%t CoefficientList[Series[E^(x/(1 - x^4)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 11 2017 *)
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(1-x^4))))
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(4*k-3)))))
%Y E.g.f.: exp(x/(1 - x^m)): A000262 (m=1), A088009 (m=2), A293493 (m=3), this sequence (m=4).
%Y Cf. A293526.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Oct 10 2017
|
