A259367 E.g.f.: exp(x-(1-x^3)^(1/3)+1).

1, 1, 1, 3, 9, 21, 161, 911, 3473, 48329, 406241, 2150171, 44216921, 491897693, 3327845249, 90934644711, 1257256962081, 10352273016081, 353351881109313, 5836715156967219, 56621346170765481, 2319460179075419941, 44545835926727113441, 497433851743810193983, 23782590451590763744689

Offset: 0

Author

Karol A. Penson and Katarzyna Gorska, Jun 25 2015

Keywords

• nonn

Crossrefs

Cf. A259239,A067622.

Programs

Mathematica

nmax = 30; CoefficientList[Series[E^(x-(1-x^3)^(1/3)+1), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 08 2021 *)

Formula

a(n) ~ n! * (exp(2) + 2*exp(1/2) * cos((4*Pi*n - 3*sqrt(3))/6)) / (3^(2/3)*Gamma(2/3)*n^(4/3)) * (1 - 3^(5/6)*Gamma(2/3)^2 / (2*Pi*n^(1/3))). - Vaclav Kotesovec, Jun 08 2021