A335643 Expansion of e.g.f. Product_{k>0} 1/(1 - tan(x)^k / k!).

1, 1, 3, 12, 71, 462, 3890, 35133, 381583, 4411870, 58623990, 826335675, 12990713482, 216027857567, 3925135187017, 75217607162053, 1552186877466271, 33678081631793270, 778592124168964502, 18867293553102673343, 483291402186818709310, 12937553749692179771301, 363847628395565829224327

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) ~ A247551 * 2^(2*n+1) * n! / Pi^(n+1). - Vaclav Kotesovec, Oct 04 2020

Mathematica

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 *)

Prog

(PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-tan(x)^k/k!)))
(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))))))

Crossrefs

Cf. A005651, A335627, A335636, A335642, A336046.

Sequence in context: A330493 A112320 A103366 * A277457 A367117 A228386

Adjacent sequences: A335640 A335641 A335642 * A335644 A335645 A335646

Keyword

nonn

Author

Seiichi Manyama, Oct 03 2020

Status

approved