A336046 Expansion of e.g.f. Product_{k>0} (1 + tan(x)^k / k!).

1, 1, 1, 6, 13, 112, 418, 4025, 23773, 237256, 2022526, 20878803, 236842838, 2567676659, 36410743437, 419956671339, 7116408372829, 87937527652592, 1724613303370022, 22889017703271151, 507452662263001722, 7236316297556572973, 178035555403835890935, 2728137658918521763201

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

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

Mathematica

max = 23; Range[0, max]! * CoefficientList[Series[Product[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(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))))))

Crossrefs

Cf. A007837, A335630, A335638, A335643, A335644.

Sequence in context: A292121 A364199 A236250 * A368633 A042285 A041070

Adjacent sequences: A336043 A336044 A336045 * A336047 A336048 A336049

Keyword

nonn

Author

Seiichi Manyama, Oct 03 2020

Status

approved