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 A053126 Binomial coefficients binomial(2*n-3,4). 12
 5, 35, 126, 330, 715, 1365, 2380, 3876, 5985, 8855, 12650, 17550, 23751, 31465, 40920, 52360, 66045, 82251, 101270, 123410, 148995, 178365, 211876, 249900, 292825, 341055, 395010, 455126, 521855, 595665, 677040, 766480 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A053123, A002492. Sequence in context: A161199 A111877 A179337 * A096743 A026697 A000910 Adjacent sequences:  A053123 A053124 A053125 * A053127 A053128 A053129 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 30 14:51 EDT 2022. Contains 354943 sequences. (Running on oeis4.)