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%I #14 Dec 02 2021 10:34:23
%S 1,1,5,31,241,2261,25501,319915,4564001,71905321,1240694101,
%T 23250921431,470598127825,10200501671101,236040247113581,
%U 5800885227542371,150850086300786241,4137020164029442385,119309846230265324581,3608164806033723494671
%N E.g.f.: exp(1/((1-x)*(1-x^2)*(1-x^3)) - 1).
%H Seiichi Manyama, <a href="/A294214/b294214.txt">Table of n, a(n) for n = 0..430</a>
%F a(n) = a(n-1) + 2*(n-1)*n*a(n-2) + (n-2)*(n-1)*(2*n+1)*a(n-3) - (n-10)*(n-3)*(n-2)*(n-1)*a(n-4) - 4*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6) + 2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-7) + 2*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-8) - (n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-10). - _Vaclav Kotesovec_, Dec 02 2021
%F a(n) ~ exp(-101/144 + 29*n^(1/4)/(36*2^(3/4)) + sqrt(n/2) + 2^(7/4)*n^(3/4)/3 - n) * n^(n - 1/8) / 2^(9/8) * (1 + 71323/(103680*2^(1/4)*n^(1/4))). - _Vaclav Kotesovec_, Dec 02 2021
%t nmax = 20; CoefficientList[Series[E^(1/((1-x)*(1-x^2)*(1-x^3)) - 1), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Dec 02 2021 *)
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(1/((1-x)*(1-x^2)*(1-x^3))-1)))
%Y Column k=3 of A294212.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 25 2017
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