A004348 Binomial coefficient C(5n, n-6).

1, 35, 780, 14190, 230300, 3478761, 50063860, 696190560, 9440350920, 125595622175, 1646492110120, 21335200040700, 273897571557780, 3489735464257595, 44186942677323600, 556608279578340080, 6981073962530525550, 87237418624987818825, 1086744939880326302940

Offset

6,2

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

Vincenzo Librandi, Table of n, a(n) for n = 6..100

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)*(2*n+3)*(n-6)*(4*n+5)*(n+1)*a(n) + 5*n*(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+27/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 08 2025

Mathematica

Table[Binomial[5n, n-6], {n, 6, 25}] (* Harvey P. Dale, Sep 23 2011 *)

Prog

(Magma) [Binomial(5*n, n-6): n in [6..30]]; // Vincenzo Librandi, Sep 24 2011
(PARI) a(n) = binomial(5*n, n-6); \\ Amiram Eldar, Sep 08 2025

Crossrefs

Sequence in context: A028196 A028208 A028194 * A028189 A028162 A028160

Adjacent sequences: A004345 A004346 A004347 * A004349 A004350 A004351

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved