A253182 The continued fraction expansion of e! (A178394).

4, 3, 1, 5, 38, 2, 1, 65, 1, 1, 2, 2, 3, 5, 1, 1, 38, 1, 1, 1, 5, 16, 1, 1, 1, 1, 5, 1, 97, 1, 1, 1, 1, 1, 1, 10, 4, 1, 6, 3, 3, 10, 6, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 4, 5, 1, 14, 2, 5, 12, 2, 2, 2, 2, 1, 3, 2, 1, 1, 2, 4, 1, 1, 6, 3, 1, 4, 2, 1, 1, 1, 1

Offset: 0

Author

Robert G. Wilson v, Mar 23 2015

Keywords

• nonn
• cofr
• easy

Comments

The increasing partial quotients (after the initial 4) are 3, 5, 38, 65, 97, 98, 239, 644, 3395, 11360, 14473, 263721, ..., .

Examples

			Gamma(e+1) = 4.2608204763570033817001212246457024649334243739593219749116...
= 4 + 1/(3 + 1/(1 + 1/(5 + 1/(38 + ...))))
= [a_0; a_1, a_2, a_3, ...] = [4; 3, 1, 5, 38, ...]
		

Crossrefs

Cf. A178394, A255196.

Programs

Mathematica

ContinuedFraction[E!, 90]

PARI

default(realprecision, 100); contfrac(gamma(exp(1)+1)) \\ Michel Marcus, Mar 24 2015