A053128 Binomial coefficients C(2*n-5,6).

7, 84, 462, 1716, 5005, 12376, 27132, 54264, 100947, 177100, 296010, 475020, 736281, 1107568, 1623160, 2324784, 3262623, 4496388, 6096454, 8145060, 10737573, 13983816, 18009460, 22957480, 28989675, 36288252, 45057474, 55525372, 67945521, 82598880, 99795696

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).

Index entries for sequences related to Chebyshev polynomials.

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

Cf. A053123, A053127.

Sequence in context: A187649 A368853 A316377 * A027819 A269895 A272496

Adjacent sequences: A053125 A053126 A053127 * A053129 A053130 A053131

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved