A010975 a(n) = binomial(n,22).

1, 23, 276, 2300, 14950, 80730, 376740, 1560780, 5852925, 20160075, 64512240, 193536720, 548354040, 1476337800, 3796297200, 9364199760, 22239974430, 51021117810, 113380261800, 244662670200, 513791607420, 1052049481860, 2104098963720, 4116715363800

Offset: 22

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Coordination sequence for 22-dimensional cyclotomic lattice Z[zeta_23].

Links

• T. D. Noe, Table of n, a(n) for n = 22..1000
• Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
• Milan Janjic, Two Enumerative Functions.
• Index entries for linear recurrences with constant coefficients, signature (23, -253, 1771, -8855, 33649, -100947, 245157, -490314, 817190, -1144066, 1352078, -1352078, 1144066, -817190, 490314, -245157, 100947, -33649, 8855, -1771, 253, -23, 1).

Crossrefs

Pascal's triangle A007318. - Zerinvary Lajos, Aug 04 2008

Cf. A001787, A242091.

Programs

Magma

[ Binomial(n,22): n in [22..80]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,22),n=22..42); # Zerinvary Lajos, Aug 04 2008

Mathematica

Binomial[Range[22,50],22]  (* Harvey P. Dale, Apr 02 2011 *)

PARI

for(n=22, 50, print1(binomial(n,22), ", ")) \\ G. C. Greubel, Nov 23 2017

Formula

a(n) = n/(n-22) * a(n-1), n > 22. - Vincenzo Librandi, Mar 26 2011

G.f.: x^22/(1-x)^23. - G. C. Greubel, Nov 23 2017

From Amiram Eldar, Dec 11 2020: (Start)

Sum_{n>=22} 1/a(n) = 22/21.

Sum_{n>=22} (-1)^n/a(n) = A001787(22)*log(2) - A242091(22)/21! = 46137344*log(2) - 42299425233749/1322685 = 0.9597667941... (End)