A004371 Binomial coefficient C(7n,n-3).

1, 28, 595, 11480, 211876, 3819816, 67945521, 1198774720, 21042072975, 368136785016, 6426898010533, 112044912118048, 1951641934005400, 33976189889821200, 591315394579074378, 10289781864706066800, 179055142158375051800, 3115999030593616524000, 54232964416333239852315

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..21.

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

a(n) ~ 7^(7*n+1/2) / (6^(6*n+7/2) * sqrt(2*Pi*n)). - Amiram Eldar, Sep 09 2025

a(n) = A004372(n)*2*(3*n+2)/(n-3). - R. J. Mathar, Mar 14 2026

D-finite with recurrence -72*(6*n-1)*(n-3)*(3*n-1)*(2*n+1)*(3*n+1)*(6*n+1)*a(n) +7*(7*n-3)*(7*n-6)*(7*n-2)*(7*n-5)*(7*n-1)*(7*n-4)*a(n-1)=0. - R. J. Mathar, Mar 14 2026

Mathematica

a[n_] := Binomial[7*n, n-3]; Array[a, 25, 3] (* Amiram Eldar, Sep 09 2025 *)

Prog

(PARI) a(n) = binomial(7*n, n-3); \\ Amiram Eldar, Sep 09 2025

Crossrefs

Sequence in context: A107397 A053110 A264459 * A283096 A089908 A038121

Adjacent sequences: A004368 A004369 A004370 * A004372 A004373 A004374

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved