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%I #15 Dec 26 2021 20:55:28
%S 1,24,351,4060,40920,376992,3262623,26978328,215553195,1677106640,
%T 12777711870,95722852680,707285522580,5166863427600,37387265592825,
%U 268367258592576,1913212193400684,13559593014190944
%N Binomial coefficient C(3n,n-7).
%D 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.
%H Robert Israel, <a href="/A004325/b004325.txt">Table of n, a(n) for n = 7..1209</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%F From _Robert Israel_, Jan 28 2018: (Start)
%F E.g.f.: x^7*hypergeom([22/3, 23/3], [11, 23/2], 27*x/4)/5040.
%F a(n+1) = (3*(3*n+1))*(3*n+2)*(n+1)/((2*(n+4))*(2*n+9)*(n-6))*a(n).
%F a(n) ~ sqrt(3/(Pi*n))*(27/4)^n/256 (End)
%p seq(binomial(3*n,n-7),n=7..50); # _Robert Israel_, Jan 28 2018
%t Table[Binomial[3n,n-7],{n,7,30}] (* _Harvey P. Dale_, Dec 04 2014 *)
%K nonn,easy
%O 7,2
%A _N. J. A. Sloane_