A004338 Binomial coefficient C(4n,n-8).

1, 36, 780, 13244, 194580, 2598960, 32468436, 386206920, 4426165368, 49280065120, 536211932256, 5727160371180, 60246643120300, 625806790696080, 6431976680401800, 65516299116620976, 662252084388541314, 6650134872937201800, 66397754897095181560, 659645433004618405800

Offset

8,2

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 = 8..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+8)*(3*n+7)*(n-8)*(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+17/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 07 2025

Mathematica

Table[Binomial[4n, n-8], {n, 8, 30}] (* Harvey P. Dale, Jul 28 2024 *)

Crossrefs

Sequence in context: A036084 A265194 A280123 * A228331 A014772 A110206

Adjacent sequences: A004335 A004336 A004337 * A004339 A004340 A004341

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved