A053126 Binomial coefficients binomial(2*n-3,4).
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
Offset: 4
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 sequences related to Chebyshev polynomials.
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
-
Magma
[Binomial(2*n-3,4): n in [4..40]]; // Vincenzo Librandi, Oct 07 2011
-
Mathematica
Table[Binomial[2*n-3,4], {n,4,50}] (* G. C. Greubel, Aug 26 2018 *) -
PARI
for(n=4,50, print1(binomial(2*n-3,4), ", ")) \\ G. C. Greubel, Aug 26 2018
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)
Comments