A010983 Binomial coefficient C(n,30).
1, 31, 496, 5456, 46376, 324632, 1947792, 10295472, 48903492, 211915132, 847660528, 3159461968, 11058116888, 36576848168, 114955808528, 344867425584, 991493848554, 2741188875414, 7309837001104, 18851684897584, 47129212243960, 114456658306760, 270533919634160
Offset: 30
Links
- T. D. Noe, Table of n, a(n) for n = 30..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 (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).
Programs
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Magma
[Binomial(n, 30): n in [30..70]]; // Vincenzo Librandi, Jun 12 2013
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Maple
seq(binomial(n,30),n=30..53);# Zerinvary Lajos, Dec 19 2008
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Mathematica
Table[Binomial[n, 30], {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *) -
PARI
x='x+O('x^50); Vec(x^30/(1-x)^31) \\ G. C. Greubel, Nov 23 2017
Formula
G.f.: x^30/(1-x)^31. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017
From Amiram Eldar, Dec 12 2020: (Start)
Sum_{n>=30} 1/a(n) = 30/29.
Comments