A306770 Decimal expansion of Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!).

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

Offset

0,1

Links

Table of n, a(n) for n=0..89.

Eric Weisstein's World of Mathematics, Exponential Integral.

Formula

Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!) = exp(1) - 1 + gamma - ExpIntegralEi[1].

From Amiram Eldar, Jun 26 2021: (Start)

Equals Sum_{k>=2} 1/A054119(k).

Equals -Integral{x=0..1} x*log(x)*exp(x) dx. (End)

Example

0.40037967700464134050027...

Prog

(PARI) exp(1) - 1 + Euler - real(-eint1(-1)) \\ Michel Marcus, Mar 09 2019

Crossrefs

Cf. A001113 (exp(1)), A001620 (gamma), A054119, A091725 (ExpIntegralEi[1]).

Sequence in context: A091467 A224861 A050443 * A308278 A308277 A278216

Adjacent sequences: A306767 A306768 A306769 * A306771 A306772 A306773

Keyword

nonn,cons

Author

Seiichi Manyama, Mar 09 2019

Status

approved