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 A039821 Numerators in Stirling expansion of middle binomial coefficient. 0
 1, 1, 10, 21, 798, 1738, 157300, 334477, 57434806, 119394366, 33601489740, 68858583810, 28797022447980, 58526378304180, 34009655736503400, 68787420596367165, 52951950764170220070 (list; graph; refs; listen; history; text; internal format)
 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 REFERENCES D. B. Tyler, D. Hickerson, unpublished correspondence, 1985-8; cf.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 Cf. A000984 (middle binomial coefficients). Sequence in context: A336748 A041198 A035318 * A109326 A080454 A226789 Adjacent sequences:  A039818 A039819 A039820 * A039822 A039823 A039824 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 22 02:03 EDT 2021. Contains 347605 sequences. (Running on oeis4.)