A039821 Numerators in Stirling expansion of middle binomial coefficient.

1, 1, 10, 21, 798, 1738, 157300, 334477, 57434806, 119394366, 33601489740, 68858583810, 28797022447980, 58526378304180, 34009655736503400, 68787420596367165, 52951950764170220070

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D. B. Tyler, D. Hickerson, unpublished correspondence, 1985-8; cf.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

Table of n, a(n) for n=1..17.

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 A369120 A080454

Adjacent sequences: A039818 A039819 A039820 * A039822 A039823 A039824

Keyword

nonn

Author

Len Smiley

Status

approved