A335636 Expansion of e.g.f. Product_{k>0} 1/(1 - tan(x)^k / k).

1, 1, 3, 13, 80, 560, 4972, 48060, 552632, 6813560, 95846728, 1435488184, 23855755040, 419889384096, 8048166402304, 162616435301824, 3531256457687168, 80497793591765120, 1953028123616286592, 49561115477458450560, 1328614915154244276224, 37134707962379971432448

Offset

0,3

Links

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

Formula

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

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

Mathematica

max = 21; Range[0, max]! * CoefficientList[Series[Product[1/(1 - Tan[x]^k/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Oct 03 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. A000182, A007841, A335627, A335635, A335638, A335643.

Sequence in context: A090364 A112935 A258377 * A366179 A201795 A308521

Adjacent sequences: A335633 A335634 A335635 * A335637 A335638 A335639

Keyword

nonn

Author

Seiichi Manyama, Oct 03 2020

Status

approved