A337153 - OEIS

A337153

a(n) = 3^n * (n!)^2 * Sum_{k=0..n} 1 / ((-3)^k * (k!)^2).

1, 2, 25, 674, 32353, 2426474, 262059193, 38522701370, 7396358663041, 1797315155118962, 539194546535688601, 195727620392454962162, 84554332009540543653985, 42869046328837055632570394, 25206999241356188711951391673, 17014724487915427380567189379274, 13067308406719048228275601443282433

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselJ(0,2*sqrt(x)) / (1 - 3*x).

a(0) = 1; a(n) = 3 * n^2 * a(n-1) + (-1)^n.

MATHEMATICA

Table[3^n n!^2 Sum[1/((-3)^k k!^2), {k, 0, n}], {n, 0, 16}]

nmax = 16; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - 3 x), {x, 0, nmax}], x] Range[0, nmax]!^2

PROG