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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. 4
0, 0, 27, 288, 2250, 15795, 105987, 696864, 4540968, 29490750, 191420427, 1243565235, 8091223647, 52739879283, 344402073027, 2253045672480, 14764068268068, 96899123172708, 636877933530303, 4191430966219038, 27617820628739718, 182176855684869243 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 10:14 EDT 2019. Contains 328345 sequences. (Running on oeis4.)