A372388 Decimal expansion of Sum_{k>=0} (k+2) / (2k+1)!.

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

Offset

1,1

Links

Table of n, a(n) for n=1..86.

Index entries for transcendental numbers.

Formula

Equals (1/e + 4*sinh(1))/2.

Equals 2* 1F2(3;3/2,2;1/4) . - R. J. Mathar, Aug 02 2024

Example

2.53434210787332407456252558627193206403434152818407...

Mathematica

s = Sum[(k + 2)/(2 k + 1)!, {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]

Prog

(PARI) exp(-1)/2 + 4*sinh(1)/2 \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A372389.

Sequence in context: A030660 A253720 A371353 * A309735 A275726 A355505

Adjacent sequences: A372385 A372386 A372387 * A372389 A372390 A372391

Keyword

nonn,cons,changed

Author

Clark Kimberling, May 12 2024

Status

approved