%I #16 Oct 04 2020 02:52:37

%S 1,1,3,12,71,462,3890,35133,381583,4411870,58623990,826335675,

%T 12990713482,216027857567,3925135187017,75217607162053,

%U 1552186877466271,33678081631793270,778592124168964502,18867293553102673343,483291402186818709310,12937553749692179771301,363847628395565829224327

%N Expansion of e.g.f. Product_{k>0} 1/(1 - tan(x)^k / k!).

%F E.g.f.: exp( Sum_{i>0} Sum_{j>0} tan(x)^(i*j)/(i*(j!)^i) ).

%F a(n) ~ A247551 * 2^(2*n+1) * n! / Pi^(n+1). - _Vaclav Kotesovec_, Oct 04 2020

%t max = 22; Range[0, max]! * CoefficientList[Series[Product[1/(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(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. A005651, A335627, A335636, A335642, A336046.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 03 2020