A004337 Binomial coefficient C(4n,n-7).

1, 32, 630, 9880, 135751, 1712304, 20358520, 231917400, 2558620845, 27540584512, 290752384208, 3022285436352, 31022118677225, 315136287090800, 3173734438530120, 31731084956648880, 315297189498738447, 3116480397122547360, 30664510802988208300, 300537206376325558640

Offset

7,2

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

Links

Seiichi Manyama, Table of n, a(n) for n = 7..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Formula

D-finite with recurrence -3*(3*n+5)*(3*n+7)*(n-7)*(n+2)*a(n) + 8*n*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1) = 0. - R. J. Mathar, Mar 19 2025

a(n) ~ 2^(8*n+1/2) / (3^(3*n+15/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 07 2025

Mathematica

Table[Binomial[4n, n-7], {n, 7, 30}] (* Harvey P. Dale, May 12 2011 *)

Crossrefs

Sequence in context: A013699 A378296 A283279 * A292880 A255262 A181240

Adjacent sequences: A004334 A004335 A004336 * A004338 A004339 A004340

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved