A004325 Binomial coefficient C(3n,n-7).

1, 24, 351, 4060, 40920, 376992, 3262623, 26978328, 215553195, 1677106640, 12777711870, 95722852680, 707285522580, 5166863427600, 37387265592825, 268367258592576, 1913212193400684, 13559593014190944

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

Robert Israel, Table of n, a(n) for n = 7..1209

Milan Janjic, Two Enumerative Functions

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

From Robert Israel, Jan 28 2018: (Start)

E.g.f.: x^7*hypergeom([22/3, 23/3], [11, 23/2], 27*x/4)/5040.

a(n+1) = (3*(3*n+1))*(3*n+2)*(n+1)/((2*(n+4))*(2*n+9)*(n-6))*a(n).

a(n) ~ sqrt(3/(Pi*n))*(27/4)^n/256 (End)

Maple

seq(binomial(3*n, n-7), n=7..50); # Robert Israel, Jan 28 2018

Mathematica

Table[Binomial[3n, n-7], {n, 7, 30}] (* Harvey P. Dale, Dec 04 2014 *)

Crossrefs

Sequence in context: A022748 A288968 A269029 * A075621 A293618 A137499

Adjacent sequences: A004322 A004323 A004324 * A004326 A004327 A004328

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved