A335637
Expansion of e.g.f. Product_{k>0} (1 + sin(x)^k / k).
Original entry on oeis.org
1, 1, 1, 4, 10, 25, 210, 978, 2336, 25265, 361424, 1557752, -1098528, 140915385, 2093367328, 10484632486, 133131785728, -1343478380255, -8738565516288, 1790935681747980, 3245598828836864, -592809746388403495, 6832010190766985216, 179327221659613996634, -5310378915096702812160
Offset: 0
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max = 24; Range[0, max]! * CoefficientList[Series[Product[1 + Sin[x]^k/k, {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Oct 03 2020 *)
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N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+sin(x)^k/k)))
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N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(i=1, N, sum(j=1, N\i, (-1)^(i+1)*sin(x)^(i*j)/(i*j^i))))))
A335642
Expansion of e.g.f. Product_{k>0} 1/(1 - sin(x)^k / k!).
Original entry on oeis.org
1, 1, 3, 9, 35, 147, 710, 3780, 21391, 136063, 932190, 6887232, 55902274, 497726270, 4711586833, 47692742905, 528539419087, 6093676850975, 73010887114406, 943925266298096, 12740929019736310, 175037826035276730, 2561985529052306447, 39817440376814520907, 622315443336146270858
Offset: 0
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max = 24; Range[0, max]! * CoefficientList[Series[Product[1/(1 - Sin[x]^k/k!), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Oct 04 2020 *)
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N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-sin(x)^k/k!)))
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N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(i=1, N, sum(j=1, N\i, sin(x)^(i*j)/(i*j!^i))))))
A336046
Expansion of e.g.f. Product_{k>0} (1 + tan(x)^k / k!).
Original entry on oeis.org
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
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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 *)
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N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+tan(x)^k/k!)))
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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))))))
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