A277461
E.g.f.: sin(x)/(1+LambertW(-x)).
Original entry on oeis.org
0, 1, 2, 11, 104, 1241, 18216, 317715, 6414848, 147107953, 3776164000, 107253230171, 3339157316736, 113070818225353, 4137170839854976, 162653198951193059, 6837934005096620032, 306093463368534049761, 14535589272368159900160, 729835620496621069643179
Offset: 0
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CoefficientList[Series[Sin[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Table[Sin[Pi*n/2] + Sum[Binomial[n, k] * Sin[Pi*(n-k)/2] * k^k, {k, 1, n}], {n, 0, 25}] (* Vaclav Kotesovec, Oct 28 2016 *)
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x = 'x + O('x^30); concat(0, Vec(serlaplace(sin(x)/(1+lambertw(-x))))) \\ Michel Marcus, Jun 12 2017
A277464
Expansion of e.g.f. cosh(x)/(1 + LambertW(-x)).
Original entry on oeis.org
1, 1, 5, 30, 281, 3400, 50557, 890120, 18101617, 417464064, 10764826421, 306893014912, 9584448407305, 325407839778944, 11933432488693549, 470087171351873280, 19796492491889197025, 887518214183286390784, 42202928616264032249701, 2121583256369642798845952
Offset: 0
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CoefficientList[Series[Cosh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Table[(1+(-1)^n + Sum[(1+(-1)^(n-k)) * Binomial[n,k] * k^k, {k, 1, n}])/2, {n, 0, 25}]
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x='x+O('x^50); Vec(serlaplace(cosh(x)/(1 + lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017
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a(n) = sum(k=0, n\2, (n-2*k)^(n-2*k)*binomial(n, 2*k)); \\ Seiichi Manyama, Feb 15 2023
A238085
Expansion of e.g.f.: -LambertW(-sinh(x)).
Original entry on oeis.org
0, 1, 2, 10, 72, 716, 9088, 140344, 2554240, 53540368, 1270296064, 33653698464, 984753299456, 31542901202112, 1097763264864256, 41247391653500800, 1664188908529156096, 71759140177774010624, 3293251384307726942208, 160272893566770148403712
Offset: 0
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CoefficientList[Series[-LambertW[-Sinh[x]],{x,0,20}],x]*Range[0,20]!
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x='x+('x^30); concat([0], Vec(serlaplace(-lambertw(-sinh(x))))) \\ G. C. Greubel, Feb 19 2018
A277476
E.g.f.: -sinh(x)*LambertW(-x).
Original entry on oeis.org
0, 0, 2, 6, 40, 340, 3936, 56714, 976704, 19535688, 444743680, 11349643822, 320813048832, 9947821243100, 335700998830848, 12246806941654770, 480247532548624384, 20144008859005187344, 899923326921333301248, 42658767419625168409814, 2138475182252830504796160
Offset: 0
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CoefficientList[Series[-Sinh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[(1 - (-1)^(n-k)) * Binomial[n, k] * k^(k-1)/2, {k, 1, n}], {n, 0, 20}]
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x='x+O('x^50); concat([0,0], Vec(serlaplace(-sinh(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 07 2017
Showing 1-4 of 4 results.