A004345 Binomial coefficient C(5n,n-3).

1, 20, 300, 4060, 52360, 658008, 8145060, 99884400, 1217566350, 14783142660, 179013799328, 2163842859360, 26123889412400, 315136287090800, 3799541229226200, 45795673964460816, 551876736990451095, 6650134872937201800, 80135221427528667400, 965708027072695321800

Offset

3,2

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

Table of n, a(n) for n=3..22.

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

a(n) ~ 5^(5*n+1/2) / (2^(8*n+15/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 08 2025

a(n) = A004346(n)*4*(n+1)/(n-3). - R. J. Mathar, Mar 14 2026

Mathematica

Table[Binomial[5n, n-3], {n, 3, 20}] (* Harvey P. Dale, Feb 13 2013 *)

Prog

(PARI) a(n) = binomial(5*n, n-3); \\ Amiram Eldar, Sep 08 2025

Crossrefs

Sequence in context: A077758 A202270 A053541 * A001755 A361577 A016190

Adjacent sequences: A004342 A004343 A004344 * A004346 A004347 A004348

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved