A337155 a(n) = 5^n * (n!)^2 * Sum_{k=0..n} 1 / ((-5)^k * (k!)^2).

1, 4, 81, 3644, 291521, 36440124, 6559222321, 1607009468644, 514243029966081, 208268427136262804, 104134213568131402001, 63001199208719498210604, 45360863430278038711634881, 38329929598584942711331474444, 37563331006613243857104844955121, 42258747382439899339242950574511124

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselJ(0,2*sqrt(x)) / (1 - 5*x).

a(0) = 1; a(n) = 5 * n^2 * a(n-1) + (-1)^n.

Mathematica

Table[5^n n!^2 Sum[1/((-5)^k k!^2), {k, 0, n}], {n, 0, 15}]
nmax = 15; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - 5 x), {x, 0, nmax}], x] Range[0, nmax]!^2

Prog

(PARI) a(n) = 5^n * (n!)^2 * sum(k=0, n, 1 / ((-5)^k * (k!)^2)); \\ Michel Marcus, Jan 28 2021

Crossrefs

Cf. A001908, A073701, A336808, A337152, A337153, A337154.

Sequence in context: A221251 A128911 A268206 * A268105 A068087 A324088

Adjacent sequences: A337152 A337153 A337154 * A337156 A337157 A337158

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 27 2021

Status

approved