A026809 a(n) = 3^n*(3^n-1)*(3^n-2)/6.

0, 1, 84, 2925, 85320, 2362041, 64304604, 1741001445, 47050068240, 1270739210481, 34313445309924, 926494403955165, 25015631334908760, 675424587904113321, 18236486750190760044, 492385348146244352085, 13294406252968671566880, 358948985507335487598561

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..690

Index entries for linear recurrences with constant coefficients, signature (39,-351,729).

Formula

a(n) = binomial(3^n, 3), n >= 0. - Zerinvary Lajos, Jan 07 2008

From Elmo R. Oliveira, Apr 09 2026: (Start)

G.f.: x*(1 + 45*x)/((1 - 27*x)*(1 - 9*x)*(1 - 3*x)).

E.g.f.: (1/6)*(2 - 3*exp(6*x) + exp(24*x))*exp(3*x).

a(n) = 3*(13*a(n-1) - 117*a(n-2) + 243*a(n-3)). (End)

Maple

seq(binomial(3^n, 3), n=0..16); # Zerinvary Lajos, Jan 07 2008

Mathematica

Binomial[3^Range[0, 20], 3] (* G. C. Greubel, Nov 08 2019 *)

Prog

(PARI) vector(21, n, binomial(3^(n-1), 3) ) \\ G. C. Greubel, Nov 08 2019
(Magma) [Binomial(3^n, 3): n in [0..20]]; // G. C. Greubel, Nov 08 2019
(SageMath) [binomial(3^n, 3) for n in (0..20)] # G. C. Greubel, Nov 08 2019
(GAP) List([0..20], n-> Binomial(3^n, 3) ); # G. C. Greubel, Nov 08 2019

Crossrefs

Subsequence of A000292.

Sequence in context: A140903 A219470 A219372 * A114253 A377726 A017800

Adjacent sequences: A026806 A026807 A026808 * A026810 A026811 A026812

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved