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A010974
a(n) = binomial(n,21).
4
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
21,2
COMMENTS
In this sequence there are no primes. - Artur Jasinski, Dec 02 2007
LINKS
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).
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.
Sum_{n>=21} (-1)^(n+1)/a(n) = A001787(21)*log(2) - A242091(21)/20! = 22020096*log(2) - 42299423848079/2771340 = 0.9580705153... (End)
MAPLE
seq(binomial(n, 21), n=21..41); # Zerinvary Lajos, Aug 04 2008
MATHEMATICA
Table[Binomial[n, 21], {n, 21, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)
PROG
(Magma) [ Binomial(n, 21): n in [21..80]]; // Vincenzo Librandi, Mar 26 2011
(PARI) for(n=21, 50, print1(binomial(n, 21), ", ")) \\ G. C. Greubel, Nov 23 2017
CROSSREFS
Pascal's triangle A007318. - Zerinvary Lajos, Aug 04 2008
Sequence in context: A028571 A162679 A325742 * A022587 A143479 A213352
KEYWORD
nonn
STATUS
approved