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

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

(PARI) a(n) = 3^n * (n!)^2 * sum(k=0, n, 1 / ((-3)^k * (k!)^2)); \\ Michel Marcus, Jan 28 2021

Crossrefs

Cf. A000180, A073701, A336805, A337152, A337154, A337155.

Sequence in context: A330767 A197084 A366038 * A119829 A059363 A216661

Adjacent sequences: A337150 A337151 A337152 * A337154 A337155 A337156

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 27 2021

Status

approved