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%I #23 Oct 04 2020 06:56:22
%S 1,1,3,13,80,560,4972,48060,552632,6813560,95846728,1435488184,
%T 23855755040,419889384096,8048166402304,162616435301824,
%U 3531256457687168,80497793591765120,1953028123616286592,49561115477458450560,1328614915154244276224,37134707962379971432448
%N Expansion of e.g.f. Product_{k>0} 1/(1 - tan(x)^k / k).
%H Vaclav Kotesovec, <a href="/A335636/b335636.txt">Table of n, a(n) for n = 0..430</a>
%F E.g.f.: exp( Sum_{i>0} Sum_{j>0} tan(x)^(i*j)/(i*j^i) ).
%F Conjecture: a(n) ~ A080130 * n * 2^(2*n+2) * n! / Pi^(n+2). - _Vaclav Kotesovec_, Oct 04 2020
%t max = 21; Range[0, max]! * CoefficientList[Series[Product[1/(1 - Tan[x]^k/k), {k, 1, max}], {x, 0, max}], x] (* _Amiram Eldar_, Oct 03 2020 *)
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-tan(x)^k/k)))
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(i=1, N, sum(j=1, N\i, tan(x)^(i*j)/(i*j^i))))))
%Y Cf. A000182, A007841, A335627, A335635, A335638, A335643.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 03 2020
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