%I #15 Oct 04 2020 03:19:38
%S 1,1,1,6,13,112,418,4025,23773,237256,2022526,20878803,236842838,
%T 2567676659,36410743437,419956671339,7116408372829,87937527652592,
%U 1724613303370022,22889017703271151,507452662263001722,7236316297556572973,178035555403835890935,2728137658918521763201
%N Expansion of e.g.f. Product_{k>0} (1 + tan(x)^k / k!).
%F E.g.f.: exp( Sum_{i>0} Sum_{j>0} (-1)^(i+1)*tan(x)^(i*j)/(i*(j!)^i) ).
%t max = 23; Range[0, max]! * CoefficientList[Series[Product[1 + Tan[x]^k/k!, {k, 1, max}], {x, 0, max}], x] (* _Amiram Eldar_, Oct 04 2020 *)
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(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, (-1)^(i+1)*tan(x)^(i*j)/(i*j!^i))))))
%Y Cf. A007837, A335630, A335638, A335643, A335644.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Oct 03 2020