A335629
Expansion of e.g.f. Product_{k>0} (1+sin(x)^k).
Original entry on oeis.org
1, 1, 2, 11, 40, 241, 1952, 13691, 96640, 1124161, 13770752, 119165771, 1373271040, 21966388081, 297353879552, 4935774720251, 71240808202240, 589721910720001, 20308058536804352, 594276723452229131, 4142005120030474240, 73558191271194967921, 5026768573876078641152, 36395755978909448444411, -115943295497314720808960
Offset: 0
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nmax = 25; CoefficientList[Series[Product[1 + Sin[x]^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 03 2020 *)
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N=40; x='x+O('x^N); Vec(serlaplace(eta(sin(x)^2)/eta(sin(x))))
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N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+sin(x)^k)))
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N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, (-sin(x))^k/(k*(sin(x)^k-1))))))
A335627
Expansion of e.g.f. Product_{k>0} 1/(1-tan(x)^k).
Original entry on oeis.org
1, 1, 4, 20, 152, 1216, 13264, 145760, 2031872, 28617856, 480749824, 8243878400, 162085486592, 3262756228096, 73483961257984, 1695754607421440, 42992308610957312, 1118097332524711936, 31487163119164063744, 910421423509984378880, 28187970433553669292032, 896242635855128514789376
Offset: 0
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nmax = 25; CoefficientList[Series[Product[1/(1 - Tan[x]^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 03 2020 *)
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N=40; x='x+O('x^N); Vec(serlaplace(1/eta(tan(x))))
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N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-tan(x)^k)))
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N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, sigma(k)*tan(x)^k/k))))
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))))))
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))))))
A347894
E.g.f.: Product_{k>=1} (1 + x^k)^tan(x).
Original entry on oeis.org
1, 0, 2, 3, 52, 110, 2690, 11676, 247952, 1434600, 37576168, 296088760, 7698854216, 78083294640, 2187100997328, 27174552638520, 806871808214016, 11698163585372736, 370098862531800000, 6300404006917434624, 208037772410558058624, 4032385785901175122560, 141272996628892396692096
Offset: 0
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N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, (1+x^k)^tan(x))))
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N=40; x='x+O('x^N); Vec(serlaplace(exp(tan(x)*sum(k=1, N, sigma(k>>valuation(k, 2))*x^k/k))))
Showing 1-5 of 5 results.