OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n >= 9) of 4 objects: u, v, z, x with repetition allowed, containing exactly nine (9) u's. - Zerinvary Lajos, Jul 02 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (30,-405,3240,-17010,61236,-153090,262440,-295245,196830,-59049).
FORMULA
a(n) = 3^n*binomial(n+9, 9).
a(n) = A027465(n+10, 10).
G.f.: 1/(1-3*x)^10.
E.g.f.: (4480 + 120960*x + 725760*x^2 + 1693440*x^3 + 1905120*x^4 + 1143072*x^5 + 381024*x^6 + 69984*x^7 + 6561*x^8 + 243*x^9)*exp(3*x)/4480. - G. C. Greubel, May 18 2021
From Amiram Eldar, Sep 22 2022: (Start)
Sum_{n>=0} 1/a(n) = 6912*log(3/2) - 784431/280.
Sum_{n>=0} (-1)^n/a(n) = 1769472*log(4/3) - 142532433/280. (End)
MAPLE
seq(3^n*binomial(n+9, 9), n=0..20); # Zerinvary Lajos, Jul 02 2008
MATHEMATICA
Table[3^n*Binomial[n+9, 9], {n, 0, 30}] (* G. C. Greubel, May 18 2021 *)
CoefficientList[Series[1/(1-3x)^10, {x, 0, 30}], x] (* or *) LinearRecurrence[ {30, -405, 3240, -17010, 61236, -153090, 262440, -295245, 196830, -59049}, {1, 30, 495, 5940, 57915, 486486, 3648645, 25019280, 159497910, 956987460}, 30] (* Harvey P. Dale, Jan 16 2022 *)
PROG
(Sage) [3^n*binomial(n+9, 9) for n in range(30)] # Zerinvary Lajos, Mar 13 2009
(Magma) [3^n*Binomial(n+9, 9): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved