A384542 Expansion of g.f. sinh(7*arctanh(14*sqrt(x)))/(98*sqrt(x)).

1, 1666, 1090054, 485318932, 176760328262, 56963958713340, 16909346921973660, 4732136004374122344, 1266899066122354262598, 327667319343098397330668, 82435716917761454374571444, 20275150472587631020453400984, 4893425028040341625551135687452, 1162305136998381407493307772297560

Offset: 0

Author

Karol A. Penson, Jun 02 2025

Keywords

• nonn

Crossrefs

Cf. A383928, A384335, A285043, A285044, A285045, A285046, A384417.

Programs

Mathematica

a[n_]:=49^n*(105 + 464*n + 704*n^2 + 512*n^3)*(2*n)!/(105*(n!)^2); Array[a,14,0] (* Stefano Spezia, Jun 02 2025 *)

Formula

a(n) = 49^n*(105 + 464*n + 704*n^2 + 512*n^3)*(2*n)!/(105*(n!)^2).

O.g.f.: (1 + 980*x + 115248*x^2 + 1075648*x^3)/(-196*x + 1)^(7/2).

E.g.f.: exp(98*x)*(BesselI(0, 98*x)*(275365888*x^3 + 5444096*x^2 + 23520*x + 15) + 224*x*BesselI(1, 98*x)*(1229312*x^2 + 18032*x + 29))/15.