A335627 Expansion of e.g.f. Product_{k>0} 1/(1-tan(x)^k).

1, 1, 4, 20, 152, 1216, 13264, 145760, 2031872, 28617856, 480749824, 8243878400, 162085486592, 3262756228096, 73483961257984, 1695754607421440, 42992308610957312, 1118097332524711936, 31487163119164063744, 910421423509984378880, 28187970433553669292032, 896242635855128514789376

Offset: 0

Author

Seiichi Manyama, Oct 02 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A000041, A000182, A335626, A335630.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Product[1/(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(1/eta(tan(x))))

PARI

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

PARI

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

Formula

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