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A004313 a(n) = binomial coefficient C(2n, n-7). 4
1, 16, 153, 1140, 7315, 42504, 230230, 1184040, 5852925, 28048800, 131128140, 600805296, 2707475148, 12033222880, 52860229080, 229911617056, 991493848554, 4244421484512, 18053528883775, 76360380541900, 321387366339585, 1346766106565880, 5621728217559090 (list; graph; refs; listen; history; text; internal format)
OFFSET
7,2
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-7)*(n+7)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Jan 24 2018
E.g.f.: BesselI(7,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 27 2019
From Amiram Eldar, Aug 27 2022: (Start)
Sum_{n>=7} 1/a(n) = 41*Pi/(9*sqrt(3)) - 24923/3465.
Sum_{n>=7} (-1)^(n+1)/a(n) = 51094*log(phi)/(5*sqrt(5)) - 7616722/3465, where phi is the golden ratio (A001622). (End)
MATHEMATICA
Table[Binomial[2n, n-7], {n, 7, 30}] (* Harvey P. Dale, Nov 27 2013 *)
PROG
(Magma) [ Binomial(2*n, n-7): n in [7..150] ]; // Vincenzo Librandi, Apr 13 2011
(PARI) a(n)=binomial(2*n, n-7) \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
Diagonal 15 of triangle A100257.
Cf. A001622.
Sequence in context: A076071 A096136 A080423 * A249981 A144499 A173763
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)