login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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D. B. Tyler, D. Hickerson, unpublished correspondence, 1985-8; cf.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

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 A080454 A226789

Adjacent sequences:  A039818 A039819 A039820 * A039822 A039823 A039824

KEYWORD

nonn

AUTHOR

Len Smiley

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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