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

Author

Hieronymus Fischer, Jan 21 2006

Keywords

• nonn

Links

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

Programs

Magma

[Binomial(3*n, n)-3*Binomial(2*n, n)+3: n in [1..40]]; // Vincenzo Librandi, Feb 09 2016

Mathematica

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

PARI

a(n) = binomial(3*n, n) - 3*binomial(2*n, n) + 3 \\ Michel Marcus, Jul 15 2013

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)