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A004317
Binomial coefficient C(2n,n-11).
1
1, 24, 325, 3276, 27405, 201376, 1344904, 8347680, 48903492, 273438880, 1471442973, 7669339132, 38910617655, 192928249296, 937845656300, 4481381406320, 21094923659355, 97997533741800, 449972009097765, 2044802197953900, 9206478467454345, 41107996877935680
OFFSET
11,2
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Milan Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - N. J. A. Sloane, Feb 13 2013
Milan Janjic and B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014), Article 14.3.5.
FORMULA
-(n-11)*(n+11)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Jan 24 2018
E.g.f.: BesselI(11,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 28 2019
From Amiram Eldar, Aug 27 2022: (Start)
Sum_{n>=11} 1/a(n) = 338662421/23279256 - 67*Pi/(9*sqrt(3)).
Sum_{n>=11} (-1)^(n+1)/a(n) = 3817214*log(phi)/(5*sqrt(5)) - 1471028205721/8953560, where phi is the golden ratio (A001622). (End)
MATHEMATICA
Table[Binomial[2n, n-11], {n, 11, 30}] (* Harvey P. Dale, Aug 02 2015 *)
PROG
(PARI) a(n)=binomial(2*n, n-11) \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
Cf. A001622.
Sequence in context: A022652 A292298 A138453 * A295250 A295649 A188779
KEYWORD
nonn,easy
STATUS
approved