A335630 Expansion of e.g.f. Product_{k>0} (1+tan(x)^k).

1, 1, 2, 14, 64, 616, 5072, 58064, 669184, 9417856, 137019392, 2294104064, 40350383104, 778782954496, 16050760435712, 352024447115264, 8269739647565824, 204097141026881536, 5360540853755052032, 147190808628196081664, 4270498402940171321344, 129024432217526266494976

Offset: 0

Author

Seiichi Manyama, Oct 02 2020

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000009, A000182, A335627, A335629.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Product[1 + Tan[x]^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 03 2020 *)

PARI

N=40; x='x+O('x^N); Vec(serlaplace(eta(tan(x)^2)/eta(tan(x))))

PARI

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

PARI

N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, (-tan(x))^k/(k*(tan(x)^k-1))))))

Formula

E.g.f.: exp( Sum_{k>0} (-tan(x))^k/(k*(tan(x)^k-1)) ).