A115246 Number of different ways to select n elements from three sets of n elements such that there is at least one element from each set.

0, 0, 27, 288, 2250, 15795, 105987, 696864, 4540968, 29490750, 191420427, 1243565235, 8091223647, 52739879283, 344402073027, 2253045672480, 14764068268068, 96899123172708, 636877933530303, 4191430966219038, 27617820628739718, 182176855684869243

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = binomial(3n, n) - 3*binomial(2n, n) + 3.

From G. C. Greubel, Feb 08 2016: (Start)

E.g.f.: 3*exp(x) - 3*exp(2*x)*BesselI_{0}(2*x) + Hypergeometric2F2[1/3,2/3; 1/2,1; 27*x/4].

G.f.: (1/((x-1)sqrt(a*b)))*[3*sqrt(a)*(1-x) - 3*sqrt(a*b) - 2*(1-x)*sqrt(b)*cos(c/3)], where a = 4-27*x, b = 1-4*x, c = arcsin(3*sqrt(3*x)/2). (End)

Mathematica

Table[Binomial[3 n, n] - 3*Binomial[2 n, n] + 3, {n, 1, 100}] (* G. C. Greubel, Feb 08 2016 *)

Prog

(PARI) a(n) = binomial(3*n, n) - 3*binomial(2*n, n) + 3 \\ Michel Marcus, Jul 15 2013
(Magma) [Binomial(3*n, n)-3*Binomial(2*n, n)+3: n in [1..40]]; // Vincenzo Librandi, Feb 09 2016

Crossrefs

Sequence in context: A224117 A251080 A049011 * A202126 A022687 A083813

Adjacent sequences: A115243 A115244 A115245 * A115247 A115248 A115249

Keyword

nonn

Author

Hieronymus Fischer, Jan 21 2006

Status

approved