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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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].

Programs

Magma

[Binomial(5*n, n-5): n in [5..40]]; // Vincenzo Librandi, Feb 01 2017

Mathematica

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

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