A004347 Binomial coefficient C(5n,n-5).

1, 30, 595, 9880, 148995, 2118760, 28989675, 386206920, 5047381560, 65033528560, 828931106355, 10477677064400, 131567066917650, 1643385429346680, 20439879147794485, 253338471349988640

Offset

5,2

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 = 5..940

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

From Ilya Gutkovskiy, Jan 31 2017: (Start)

E.g.f.: (1/120)*x^5*4F4(26/5,27/5,28/5,29/5; 13/2,27/4,7,29/4; 3125*x/256).

a(n) ~ 5^(5*n+1/2)/(sqrt(Pi*n)*2^(8*n+23/2)). (End)

D-finite with recurrence -8*(4*n+5)*(n-5)*(2*n+1)*(4*n+3)*(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

Mathematica

Table[Binomial[5 n, n - 5], {n, 5, 40}] (* Vincenzo Librandi, Feb 01 2017 *)

Prog

(Magma) [Binomial(5*n, n-5): n in [5..40]]; // Vincenzo Librandi, Feb 01 2017
(PARI) a(n) = binomial(5*n, n-5); \\ Amiram Eldar, Sep 08 2025

Crossrefs

Sequence in context: A028003 A024999 A024778 * A028052 A024445 A026308

Adjacent sequences: A004344 A004345 A004346 * A004348 A004349 A004350

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved