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 A010975 a(n) = binomial(n,22). 3
 1, 23, 276, 2300, 14950, 80730, 376740, 1560780, 5852925, 20160075, 64512240, 193536720, 548354040, 1476337800, 3796297200, 9364199760, 22239974430, 51021117810, 113380261800, 244662670200, 513791607420, 1052049481860, 2104098963720, 4116715363800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 22,2 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). 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) MAPLE (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 *) PROG (Magma) [ Binomial(n, 22): n in [22..80]]; // Vincenzo Librandi, Mar 26 2011 (PARI) for(n=22, 50, print1(binomial(n, 22), ", ")) \\ G. C. Greubel, Nov 23 2017 CROSSREFS Pascal's triangle A007318. - Zerinvary Lajos, Aug 04 2008 Cf. A001787, A242091. Sequence in context: A161930 A162365 A162680 * A022588 A268992 A199031 Adjacent sequences: A010972 A010973 A010974 * A010976 A010977 A010978 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified March 3 02:27 EST 2024. Contains 370499 sequences. (Running on oeis4.)