A335635
Expansion of e.g.f. Product_{k>0} 1/(1 - sin(x)^k / k).
Original entry on oeis.org
1, 1, 3, 10, 44, 215, 1252, 7992, 56024, 438341, 3672328, 32587366, 318586880, 3325053147, 35115462592, 407034567076, 5198294627456, 63965057355305, 824995119961984, 12611299833296898, 184189806819806720, 2590874864719588031, 44912343151409875456, 728583107189913021328, 11458864344772729650176
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 03 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))))))
A335638
Expansion of e.g.f. Product_{k>0} (1 + tan(x)^k / k).
Original entry on oeis.org
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
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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 *)
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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))))))
A335643
Expansion of e.g.f. Product_{k>0} 1/(1 - tan(x)^k / k!).
Original entry on oeis.org
1, 1, 3, 12, 71, 462, 3890, 35133, 381583, 4411870, 58623990, 826335675, 12990713482, 216027857567, 3925135187017, 75217607162053, 1552186877466271, 33678081631793270, 778592124168964502, 18867293553102673343, 483291402186818709310, 12937553749692179771301, 363847628395565829224327
Offset: 0
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max = 22; Range[0, max]! * CoefficientList[Series[Product[1/(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(1/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, tan(x)^(i*j)/(i*j!^i))))))
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