A004370 Binomial coefficient C(7n,n-2).

1, 21, 378, 6545, 111930, 1906884, 32468436, 553270671, 9440350920, 161322559475, 2761025887620, 47325339895743, 812325612855848, 13961746143269400, 240260199935164200, 4139207762053520646, 71385361686398338425, 1232320684266463591800, 21292660042389712914000

Offset

2,2

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=2..20.

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+5/2) * sqrt(2*Pi*n)). - Amiram Eldar, Sep 09 2025

D-finite with recurrence 72*(n-2)*(6*n-1)*(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

a(n) = A004371(n)*3*(2*n+1)/(n-2). - R. J. Mathar, Mar 14 2026

Mathematica

Table[Binomial[7n, n-2], {n, 2, 20}] (* Harvey P. Dale, Mar 16 2012 *)

Prog

(PARI) a(n) = binomial(7*n, n-2); \\ Amiram Eldar, Sep 09 2025

Crossrefs

Sequence in context: A218763 A181364 A134494 * A001881 A240683 A108740

Adjacent sequences: A004367 A004368 A004369 * A004371 A004372 A004373

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved