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A336046
Expansion of e.g.f. Product_{k>0} (1 + tan(x)^k / k!).
3
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 03 2020
STATUS
approved