A302605
a(n) = n! * [x^n] exp(n*x)*arcsin(x).
Original entry on oeis.org
0, 1, 4, 28, 272, 3384, 51300, 917064, 18884672, 440168832, 11454902500, 329208395264, 10355322975120, 353851897861760, 13052503620917124, 516917167506777600, 21875427250996723968, 985164766018898243584, 47043119138733155306052, 2374168079889664129576960
Offset: 0
Cf.
A001818,
A115416,
A291482,
A293191,
A302583,
A302584,
A302585,
A302586,
A302587,
A302606,
A302608,
A302609.
-
Table[n! SeriesCoefficient[Exp[n x] ArcSin[x], {x, 0, n}], {n, 0, 19}]
A302609
a(n) = n! * [x^n] exp(n*x)*arctanh(x).
Original entry on oeis.org
0, 1, 4, 29, 288, 3649, 56160, 1017029, 21181440, 498682881, 13095232000, 379443829709, 12025239367680, 413761766695809, 15360425115176960, 611958601019294325, 26042588632355176448, 1179009749826940037889, 56579126414696034729984, 2868848293506101088635389
Offset: 0
Cf.
A010050,
A291484,
A293193,
A302583,
A302584,
A302585,
A302586,
A302587,
A302605,
A302606,
A302608.
-
Table[n! SeriesCoefficient[Exp[n x] ArcTanh[x], {x, 0, n}], {n, 0, 19}]
nmax = 20; CoefficientList[Series[Log[(1 - LambertW[-x])/(1 + LambertW[-x])] / (2*(1 + LambertW[-x])), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 09 2019 *)
A302606
a(n) = n! * [x^n] exp(n*x)*arcsinh(x).
Original entry on oeis.org
0, 1, 4, 26, 240, 2884, 42660, 748544, 15185856, 349574544, 9000902500, 256293989984, 7996078704240, 271246034903232, 9939835626507332, 391303051339622400, 16469438021801262848, 737992773619777599744, 35077254665501330210628, 1762671472887447792620032
Offset: 0
Cf.
A001818,
A002866,
A291483,
A302583,
A302584,
A302585,
A302586,
A302587,
A302605,
A302608,
A302609.
-
Table[n! SeriesCoefficient[Exp[n x] ArcSinh[x], {x, 0, n}], {n, 0, 19}]
Showing 1-3 of 3 results.