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A010995 Binomial coefficient C(n,42). 4
1, 43, 946, 14190, 163185, 1533939, 12271512, 85900584, 536878650, 3042312350, 15820024220, 76223753060, 343006888770, 1451182990950, 5804731963800, 22057981462440, 79960182801345, 277508869722315, 925029565741050, 2969831763694950, 9206478467454345 (list; graph; refs; listen; history; text; internal format)
OFFSET
42,2
COMMENTS
Coordination sequence for 42-dimensional cyclotomic lattice Z[zeta_43].
LINKS
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 (43, -903, 12341, -123410, 962598, -6096454, 32224114, -145008513, 563921995, -1917334783, 5752004349, -15338678264, 36576848168, -78378960360, 151532656696, -265182149218, 421171648758, -608359048206, 800472431850, -960566918220, 1052049481860, -1052049481860, 960566918220, -800472431850, 608359048206, -421171648758, 265182149218, -151532656696, 78378960360, -36576848168, 15338678264, -5752004349, 1917334783, -563921995, 145008513, -32224114, 6096454, -962598, 123410, -12341, 903, -43, 1).
FORMULA
G.f.: x^42/(1-x)^43. - Zerinvary Lajos, Dec 20 2008
From Amiram Eldar, Dec 15 2020: (Start)
Sum_{n>=42} 1/a(n) = 42/41.
Sum_{n>=42} (-1)^n/a(n) = A001787(42)*log(2) - A242091(42)/41! = 92358976733184*log(2) - 41737723319039140166101476641/651964850415450 = 0.9777363438... (End)
MAPLE
seq(binomial(n, 42), n=42..57); # Zerinvary Lajos, Dec 20 2008
MATHEMATICA
Table[Binomial[n, 42], {n, 42, 70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)
PROG
(Magma) [Binomial(n, 42): n in [42..70]]; // Vincenzo Librandi, Jun 12 2013
CROSSREFS
Sequence in context: A161668 A162181 A162412 * A253915 A288031 A265658
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 23 14:50 EDT 2024. Contains 372763 sequences. (Running on oeis4.)