A010965 a(n) = binomial(n,12).

1, 13, 91, 455, 1820, 6188, 18564, 50388, 125970, 293930, 646646, 1352078, 2704156, 5200300, 9657700, 17383860, 30421755, 51895935, 86493225, 141120525, 225792840, 354817320, 548354040, 834451800, 1251677700, 1852482996, 2707475148, 3910797436, 5586853480

Offset

12,2

Comments

Coordination sequence for 12-dimensional cyclotomic lattice Z[zeta_13].

In this sequence only 13 is prime. - Artur Jasinski, Dec 02 2007

Links

T. D. Noe, Table of n, a(n) for n = 12..1000

Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.

Index entries for linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

Formula

a(n) = A110555(n+1,12). - Reinhard Zumkeller, Jul 27 2005

a(n+11) = n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)(n+11)/12!. - Artur Jasinski, Dec 02 2007, R. J. Mathar, Jul 07 2009

G.f.: x^12/(1-x)^13. - Zerinvary Lajos, Aug 06 2008, R. J. Mathar, Jul 07 2009

From Amiram Eldar, Dec 10 2020: (Start)

Sum_{n>=12} 1/a(n) = 12/11.

Sum_{n>=12} (-1)^n/a(n) = A001787(12)*log(2) - A242091(12)/11! = 24576*log(2) - 3934820/231 = 0.9322955884... (End)

Maple

seq(binomial(n, 12), n=12..36); # Zerinvary Lajos, Aug 06 2008

Mathematica

Table[Binomial[n, 12], {n, 12, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)

Prog

(Magma) [Binomial(n, 12): n in [12..100]]; // Vincenzo Librandi, Apr 22 2011
(PARI) for(n=12, 50, print1(binomial(n, 12), ", ")) \\ G. C. Greubel, Aug 31 2017

Crossrefs

Cf. A000581, A010966, A010967, A001787, A242091.

Sequence in context: A247611 A008505 A008495 * A221144 A022578 A090020

Adjacent sequences: A010962 A010963 A010964 * A010966 A010967 A010968

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Some formulas referring to other offsets corrected by R. J. Mathar, Jul 07 2009

Status

approved