OFFSET
1,3
COMMENTS
a(j) is exactly divisible by 2^([ binary digit sum of j ]-1) (see reference).
REFERENCES
D. B. Tyler, D. Hickerson, unpublished correspondence, 1985-8; cf. above reference.
LINKS
R. Richberg, D. E. Knuth (independently), Problem 6581: The asymptotic expansion of the Middle Binomial Coefficient, Amer. Math. Monthly, 97 (7) 1990, 626-630.
FORMULA
2*sqrt(x)*GAMMA(x+(1/2))/GAMMA(x+1) = 1 - 1/(16*x) - Sum_{j>=2} (a(j)*((16*x)^(-j))*((-1)^floor(j/2))).
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved