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A010971 a(n) = binomial(n,18). 7
1, 19, 190, 1330, 7315, 33649, 134596, 480700, 1562275, 4686825, 13123110, 34597290, 86493225, 206253075, 471435600, 1037158320, 2203961430, 4537567650, 9075135300, 17672631900, 33578000610, 62359143990, 113380261800, 202112640600, 353697121050, 608359048206 (list; graph; refs; listen; history; text; internal format)
OFFSET

18,2

COMMENTS

Coordination sequence for 18-dimensional cyclotomic lattice Z[zeta_19].

Product of 18 consecutive numbers divided by 18!. - Artur Jasinski, Dec 02 2007

In this sequence only 19 is prime. - Artur Jasinski, Dec 02 2007

With a different offset, number of n-permutations (n>=18) of 2 objects: u,v, with repetition allowed, containing exactly (18) u's. - Zerinvary Lajos, Aug 04 2008

LINKS

T. D. Noe, Table of n, a(n) for n = 18..1000

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

Milan Janjic, Two Enumerative Functions [Broken link]

FORMULA

a(n+17) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)*(n+8)*(n+9)*(n+10)*(n+11)*(n+12)*(n+13)*(n+14)*(n+15)*(n+16)*(n+17)/18!. - Artur Jasinski, Dec 02 2007, R. J. Mathar, Jul 07 2009

G.f.: x^18/(1-x)^19. - Zerinvary Lajos, Aug 04 2008, R. J. Mathar, Jul 07 2009

MAPLE

(Maple) seq(binomial(n, 18), n=18..38); # Zerinvary Lajos, Aug 04 2008

MATHEMATICA

Table[n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)(n+11)(n+12)(n+13)(n+14)(n+15)(n+16)(n+17)/18!, {n, 1, 100}] (* Artur Jasinski, Dec 02 2007 *)

Table[Binomial[n, 18], {n, 18, 50}] (* Vincenzo Librandi, Aug 08 2017 *)

PROG

(MAGMA) [Binomial(n, 18): n in [18..50]]; // Vincenzo Librandi, Aug 08 2017

(PARI) for(n=18, 50, print1(binomial(n, 18), ", ")) \\ G. C. Greubel, Nov 23 2017

CROSSREFS

Sequence in context: A121039 A162639 A247614 * A022584 A140569 A142268

Adjacent sequences:  A010968 A010969 A010970 * A010972 A010973 A010974

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Some formulas adjusted to the offset by R. J. Mathar, Jul 07 2009

STATUS

approved

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Last modified November 17 07:44 EST 2018. Contains 317275 sequences. (Running on oeis4.)