A062995 Doubly exponentiate the Bessel function I(0,2*sqrt(z)).

1, 1, 5, 49, 789, 18741, 612383, 26218956, 1419303189, 94531262917, 7582017897795, 719690829785016, 79691175192777855, 10170046938232956048, 1480481369981439216732, 243659154929530351237884, 44987315567879408248084629, 9254611189980167520327621253

Offset: 0

Author

Karol A. Penson, Jun 28 2001

Keywords

• easy
• nonn

Links

• Index entries for sequences related to Bessel functions or polynomials

Crossrefs

Cf. A023998.

Programs

Mathematica

nmax = 20; CoefficientList[Series[E^(-1 + E^(-1 + BesselI[0, 2*Sqrt[x]])), {x, 0, nmax}], x] * Range[0, nmax]!^2 (* Vaclav Kotesovec, Jun 09 2019 *)

Formula

Hypergeometric generating function for a(n): exp(exp(BesselI(0, 2*sqrt(z))-1)-1) = Sum_{n>=0} a(n)*z^n/(n!)^2.

Extensions

More terms from Vaclav Kotesovec, Jun 09 2019