A334379 Decimal expansion of Sum_{k>=0} 1/((2*k)!)^2.

1, 2, 5, 1, 7, 3, 8, 0, 4, 0, 7, 3, 8, 6, 5, 1, 4, 6, 7, 7, 4, 4, 5, 1, 5, 9, 4, 7, 7, 3, 0, 7, 4, 0, 9, 8, 9, 5, 5, 5, 4, 9, 7, 7, 9, 2, 5, 0, 2, 0, 3, 3, 3, 2, 8, 5, 9, 9, 5, 9, 4, 7, 2, 8, 8, 3, 7, 5, 7, 9, 6, 5, 0, 5, 0, 0, 3, 4, 3, 5, 2, 3, 8, 7, 2, 1, 6, 4, 3, 0, 0, 2, 0, 4, 9, 5, 7, 6, 3, 2, 5, 1, 6, 9, 1, 6, 2, 8, 2, 7

Offset

1,2

Links

Table of n, a(n) for n=1..110.

Index entries for sequences related to Bessel functions or polynomials

Formula

Equals (BesselI(0,2) + BesselJ(0,2))/2.

Continued fraction: 1 + 1/(4 - 4/(145 - 144/(901 - ... - P(n-1)/((P(n) + 1) - ... )))), where P(n) = (2*n*(2*n - 1))^2. - Peter Bala, Feb 22 2024

Example

1/0!^2 + 1/2!^2 + 1/4!^2 + 1/6!^2 + ... = 1.25173804073865146774451594773...

Mathematica

RealDigits[(BesselI[0, 2] + BesselJ[0, 2])/2, 10, 110] [[1]]

Prog

(PARI) suminf(k=0, 1/((2*k)!)^2) \\ Michel Marcus, Apr 26 2020
(PARI) (besseli(0, 2) + besselj(0, 2))/2 \\ Michel Marcus, Apr 26 2020

Crossrefs

Cf. A010050, A049470, A070910, A073743, A091681, A197036, A334378.

Sequence in context: A321966 A304822 A165278 * A106619 A173630 A060789

Adjacent sequences: A334376 A334377 A334378 * A334380 A334381 A334382

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Apr 25 2020

Status

approved