A085115 - OEIS

A085115

Numerator of G(n) = Sum_{k=1..n} (1/(2*2^k)) * Sum_{j=0..k-1} 1/binomial(2^(k-j)+j,j).

1, 5, 241, 1561, 96029, 8580709, 1707931151, 147403551109, 1271289370866337, 18501833565256581935, 1745474502799550774494057, 35091068020856449153974443861, 12840452368911027932139293073746831113, 8314558018146658445763489072765515271142169

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..14.

David H. Bailey and Richard E. Crandall, Random generators and normal numbers, Experimental Mathematics, Vol. 11, No. 4 (2002), pp. 527-546.

M. Beeler, R. W. Gosper and R. Schroeppel, HAKMEM, Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972, Item 120, page 55. Also HTML transcription.

FORMULA

Limit_{n-->oo} G(n) = gamma = 0.5772... (A001620).

PROG

(PARI) a(n)=numerator(sum(k=1, n, 1/2^k/2*sum(j=0, k-1, 1/binomial(2^(k-j)+j, j))))

CROSSREFS

Cf. A001620, A085116 (denominators).

Sequence in context: A230885 A142732 A242625 * A317165 A327582 A144999

Adjacent sequences: A085112 A085113 A085114 * A085116 A085117 A085118

KEYWORD

frac,nonn

AUTHOR

Benoit Cloitre, Aug 10 2003

EXTENSIONS

Offset 1 and more terms from Michel Marcus, Nov 17 2025

STATUS

approved