A384335 Expansion of g.f.: cosh(7*arctanh(6*sqrt(x))).

1, 882, 150822, 14431284, 1052738694, 65805858972, 3724625506140, 196735568051880, 9876433300259526, 476865669055691916, 22326189769485093492, 1019514155600973935448, 45604820017276687744668, 2004918589790139365901720, 86848896758228990302070520, 3714470212008822424691576400

Offset: 0

Author

Karol A. Penson, May 26 2025

Keywords

• nonn

Crossrefs

Cf. A383928.

Programs

Mathematica

CoefficientList[Series[Cosh[7*ArcTanh[6*Sqrt[x]]],{x,0,15}],x] (* Stefano Spezia, May 26 2025 *)

Formula

a(n) = 9^n*(512*n^3 + 64*n^2 + 144*n + 15)*(2*n)!/(15*(n!)^2).

G.f.: (1 + 756*x + 45360*x^2 + 326592*x^3)/(-36*x + 1)^(7/2).

E.g.f.: (1/5)*exp(18*x)*((5 + 4320*x + 290304*x^2 + 3981312*x^3)*BesselI(0,18*x)+((864*x + 179712*x^2 + 3981312*x^3)*BesselI(1,18*x))).