A004332 a(n) = C(4n,n-2).

1, 12, 120, 1140, 10626, 98280, 906192, 8347680, 76904685, 708930508, 6540715896, 60403728840, 558383307300, 5166863427600, 47855699958816, 443643407165376, 4116305022165108, 38223742100828400, 355214207837288800, 3303384274321653060, 30741195448351502730

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

Vincenzo Librandi, Table of n, a(n) for n = 2..200

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

G.f.: g*(g-1)^2/(4-3*g) where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 17 2011

D-finite with recurrence -3*(3*n+2)*(n-2)*(3*n+1)*a(n) + 8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1) = 0. - R. J. Mathar, May 27 2014

a(n) ~ 2^(8*n+1/2) / (3^(3*n+5/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 07 2025

a(n) = A004333(n)*3*(n+1)/(n-2). - R. J. Mathar, Mar 14 2026

Mathematica

Table[Binomial[4n, n-2], {n, 2, 20}]  (* Harvey P. Dale, Apr 11 2011 *)

Prog

(PARI) a(n) = binomial(4*n, n-2); \\ Michel Marcus, May 10 2020

Crossrefs

Cf. A002293.

Sequence in context: A291391 A115902 A277491 * A129329 A266393 A129332

Adjacent sequences: A004329 A004330 A004331 * A004333 A004334 A004335

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved