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A039821
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Numerators in Stirling expansion of middle binomial coefficient.
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0
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1, 1, 10, 21, 798, 1738, 157300, 334477, 57434806, 119394366, 33601489740, 68858583810, 28797022447980, 58526378304180, 34009655736503400, 68787420596367165, 52951950764170220070
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(j) exactly divisible by 2^([ binary digit sum of j ]-1) (see reference)
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REFERENCES
| R. Richberg, D. E. Knuth (independently), The asymptotic expansion of the Middle Binomial Coefficient, Amer. Math. Monthly, 97 (7) 1988, 626-630.
D. B. Tyler, D. Hickerson, unpublished correspondence, 1985-8; cf. above reference.
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FORMULA
| 2sqrt(x)GAMMA(x+(1/2))/GAMMA(x+1)=1-(1/16x)-sum(a(j)*[ (16x)^(-j) ]*[ (-1)^floor(j/2) ], j=2..infinity)
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CROSSREFS
| Sequence in context: A110418 A041198 A035318 * A109326 A080454 A110367
Adjacent sequences: A039818 A039819 A039820 * A039822 A039823 A039824
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KEYWORD
| nonn
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AUTHOR
| Leonard Smiley (smiley(AT)math.uaa.alaska.edu)
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