OFFSET
6,1
COMMENTS
a(n) = A053123(n,6), n >= 6; a(n) = 0, n=0..5, (seventh column of shifted Chebyshev's S-triangle, decreasing order).
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 = 6..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 Janjić, 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 (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = binomial(2*n-5, 6) if n >= 6 else 0.
G.f.: (7+35*x+21*x^2+x^3)/(1-x)^7.
E.g.f.: (18900 - 16380*x + 6975*x^2 - 1935*x^3 + 390*x^4 - 60*x^5 + 8*x^6)*exp(x)/90. - G. C. Greubel, Aug 26 2018
a(n) = (n-5)*(n-4)*(n-3)*(2*n-9)*(2*n-7)*(2*n-5)/90. - Wesley Ivan Hurt, Mar 25 2020
From Amiram Eldar, Oct 21 2022: (Start)
Sum_{n>=6} 1/a(n) = 667/10 - 96*log(2).
Sum_{n>=6} (-1)^n/a(n) = 273/10 - 6*Pi - 12*log(2). (End)
MATHEMATICA
Table[Binomial[2*n-5, 6], {n, 6, 50}] (* G. C. Greubel, Aug 26 2018 *)
PROG
(Magma) [Binomial(2*n-5, 6): n in [6..40]]; // Vincenzo Librandi, Oct 07 2011
(PARI) for(n=6, 50, print1(binomial(2*n-5, 6), ", ")) \\ G. C. Greubel, Aug 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved