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A004315
a(n) = binomial coefficient C(2n, n-9).
3
1, 20, 231, 2024, 14950, 98280, 593775, 3365856, 18156204, 94143280, 472733756, 2311801440, 11058116888, 51915526432, 239877544005, 1093260079344, 4923689695575, 21945588357420, 96926348578605, 424655979547800, 1847253511032930, 7984465725343800, 34315056105966195
OFFSET
9,2
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, 2013. - From 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-9)*(n+9)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Dec 10 2013
E.g.f.: BesselI(9,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 27 2019
From Amiram Eldar, Aug 27 2022: (Start)
Sum_{n>=9} 1/a(n) = 2*Pi/(9*sqrt(3)) + 7457/11440.
Sum_{n>=9} (-1)^(n+1)/a(n) = 453564*log(phi)/(5*sqrt(5)) - 14069064271/720720, where phi is the golden ratio (A001622). (End)
MATHEMATICA
Table[Binomial[2*n, n-9], {n, 9, 30}] (* Amiram Eldar, Aug 27 2022 *)
PROG
(Magma) [ Binomial(2*n, n-9): n in [9..150] ]; // Vincenzo Librandi, Apr 13 2011
(PARI) a(n)=binomial(2*n, n-9) \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
Cf. A001622.
Sequence in context: A023018 A073386 A022648 * A253010 A074334 A163004
KEYWORD
nonn,easy
STATUS
approved