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
A277498
E.g.f.: -LambertW(-sin(x)).
Original entry on oeis.org
0, 1, 2, 8, 56, 536, 6528, 96592, 1683072, 33760576, 766283264, 19417068032, 543351873536, 16642224306176, 553782090473472, 19893884376859648, 767355755629215744, 31631864049541107712, 1387750771948607504384, 64561526675221208563712
Offset: 0
-
CoefficientList[Series[-LambertW[-Sin[x]], {x, 0, 20}], x] * Range[0, 20]!
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x='x+O('x^50); concat([0], Vec(serlaplace(- lambertw(-sin(x))))) \\ G. C. Greubel, Nov 08 2017
A277477
E.g.f.: -cos(x)*LambertW(-x).
Original entry on oeis.org
0, 1, 2, 6, 52, 540, 6846, 104832, 1883848, 38889360, 907247770, 23608391840, 678039307452, 21305543325248, 727095737061526, 26781816978470400, 1059020025979194128, 44746083421419997440, 2011929587198990154162, 95918808101232854969856
Offset: 0
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CoefficientList[Series[-Cos[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[Binomial[n, k] * Cos[Pi*(n-k)/2] * k^(k-1), {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)
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x='x+O('x^50); concat([0], Vec(serlaplace(-cos(x)*lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017
Showing 1-3 of 3 results.