A334378 Decimal expansion of Sum_{k>=0} 1/((2*k+1)!)^2.

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

Offset

1,3

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.

Example

1/1!^2 + 1/3!^2 + 1/5!^2 + 1/7!^2 + ... = 1.027847261597415799692...
Continued fraction: 1 + 1/(36 - 36/(401 - 400/(1765 - ... - P(n-1)/((P(n) + 1) - ... )))), where P(n) = (2*n*(2*n + 1))^2 for n >= 1. - Peter Bala, Feb 22 2024

Mathematica

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

Prog

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

Crossrefs

Cf. A009445, A049469, A070910, A073742, A091681, A197036, A334379.

Sequence in context: A316252 A202355 A202357 * A329406 A360441 A019731

Adjacent sequences: A334375 A334376 A334377 * A334379 A334380 A334381

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Apr 25 2020

Status

approved