A010974 a(n) = binomial(n,21).
1, 22, 253, 2024, 12650, 65780, 296010, 1184040, 4292145, 14307150, 44352165, 129024480, 354817320, 927983760, 2319959400, 5567902560, 12875774670, 28781143380, 62359143990, 131282408400, 269128937220, 538257874440, 1052049481860, 2012616400080, 3773655750150
Offset: 21
Keywords
Links
- T. D. Noe, Table of n, a(n) for n = 21..1000
- Milan Janjic, Two Enumerative Functions.
- Index entries for linear recurrences with constant coefficients, signature (22,-231,1540,-7315,26334,-74613,170544,-319770,497420,-646646,705432,-646646,497420,-319770,170544,-74613,26334,-7315,1540,-231,22,-1).
Crossrefs
Pascal's triangle A007318. - Zerinvary Lajos, Aug 04 2008
Programs
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Magma
[ Binomial(n,21): n in [21..80]]; // Vincenzo Librandi, Mar 26 2011
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Maple
seq(binomial(n,21),n=21..41); # Zerinvary Lajos, Aug 04 2008
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Mathematica
Table[Binomial[n,21],{n,21,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *) -
PARI
for(n=21, 50, print1(binomial(n,21), ", ")) \\ G. C. Greubel, Nov 23 2017
Formula
a(n) = 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)*(n+18)*(n+19)*(n+20) / 21!. - Artur Jasinski, Dec 02 2007
a(n) = n/(n-21) * a(n-1), n > 21. - Vincenzo Librandi, Mar 26 2011
From Amiram Eldar, Dec 11 2020: (Start)
Sum_{n>=21} 1/a(n) = 21/20.
Comments