A058299 Sum of terms in simple continued fraction for Sum_{k=0..n} 1/k!.

1, 2, 4, 5, 10, 15, 20, 16, 38, 30, 67, 49, 63, 80, 92, 139, 173, 99, 127, 159, 190, 198, 423, 198, 259, 221, 326, 631, 394, 273, 280, 341, 359, 397, 539, 418, 518, 533, 662, 3502, 735, 815, 701, 706, 611, 839, 793, 768, 781, 983, 858, 1035, 883, 3476, 1154

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..3300

Example

a(3) = 2 + 1 + 2 = 5 because 1/0! + 1/1! + 1/2! + 1/3! = 8/3 = 2 + 1/(1 + 1/2).

Maple

seq(convert(numtheory:-cfrac(add(1/k!, k=0..n), quotients), `+`), n=0..100); # Robert Israel, Aug 29 2018

Prog

(PARI) a(n) = vecsum(contfrac(sum(k=0, n, 1/k!))); \\ Michel Marcus, Aug 29 2018

Crossrefs

Cf. A069880 (number of summands).

Sequence in context: A272622 A097133 A023165 * A191616 A319909 A276281

Adjacent sequences: A058296 A058297 A058298 * A058300 A058301 A058302

Keyword

easy,nonn,look

Author

Leroy Quet, Dec 07 2000

Status

approved