OFFSET
4,1
COMMENTS
Number of intersections of diagonals in the interior of regular (2n-3)-gon. - Philippe Deléham, Jun 07 2013
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 4..200
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, Two Enumerative Functions University of Banja Luka (Bosnia and Herzegovina, 2017).
Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = binomial(2*n-3, 4) if n >= 4 else 0;
G.f.: (5+10*x+x^2)/(1-x)^5.
a(n) = A053123(n,4), n >= 4; a(n) = 0, n=0..3 (fifth column of shifted Chebyshev's S-triangle, decreasing order).
a(n) = A006561(2n-3). - Philippe Deléham, Jun 07 2013
E.g.f.: (90 - 84*x + 39*x^2 - 12*x^3 + 4*x^4)*exp(x)/6. - G. C. Greubel, Aug 26 2018
From Amiram Eldar, Jan 04 2022: (Start)
Sum_{n>=4} 1/a(n) = 34/3 - 16*log(2).
Sum_{n>=4} (-1)^n/a(n) = 2*Pi - 4*log(2) - 10/3. (End)
MATHEMATICA
Table[Binomial[2*n-3, 4], {n, 4, 50}] (* G. C. Greubel, Aug 26 2018 *)
PROG
(Magma) [Binomial(2*n-3, 4): n in [4..40]]; // Vincenzo Librandi, Oct 07 2011
(PARI) for(n=4, 50, print1(binomial(2*n-3, 4), ", ")) \\ G. C. Greubel, Aug 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved