A004349 Binomial coefficient C(5n,n-7).

1, 40, 990, 19600, 341055, 5461512, 82598880, 1198774720, 16871053725, 231900297200, 3129162672636, 41604694413840, 546585072715045, 7110542499799200, 91748617512913200, 1175759825268299040, 14980162794189827475, 189916591435396829640, 2397508365882117864750

Offset

7,2

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=7..25.

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+5)*(n-7)*(2*n+3)*(4*n+7)*(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+31/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 08 2025

Mathematica

Table[Binomial[5n, n-7], {n, 7, 30}] (* Harvey P. Dale, Nov 04 2016 *)

Prog

(PARI) a(n) = binomial(5*n, n-7); \\ Amiram Eldar, Sep 08 2025

Crossrefs

Sequence in context: A279582 A004339 A172510 * A016092 A028228 A165380

Adjacent sequences: A004346 A004347 A004348 * A004350 A004351 A004352

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved