A335638 Expansion of e.g.f. Product_{k>0} (1 + tan(x)^k / k).

1, 1, 1, 7, 22, 190, 1170, 11646, 109520, 1289168, 16018064, 223757840, 3407971488, 55709905056, 998011344928, 18778681069024, 385316251841536, 8225863823985664, 189755182485906432, 4538893733746003968, 116147781156885837824, 3078530007519830730752, 86521073899573883088896

Offset: 0

Author

Seiichi Manyama, Oct 03 2020

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..430

Crossrefs

Cf. A000182, A007838, A335630, A335636, A335637, A336046.

Programs

Mathematica

max = 22; Range[0, max]! * CoefficientList[Series[Product[1 + Tan[x]^k/k, {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Oct 03 2020 *)

PARI

N=40; x='x+O('x^N); Vec(serlaplace(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, (-1)^(i+1)*tan(x)^(i*j)/(i*j^i))))))

Formula

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

Conjecture: a(n) ~ A080130 * 2^(2*n+1) * n! / Pi^(n+1). - Vaclav Kotesovec, Oct 04 2020