OFFSET
5,1
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 = 5..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 (6,-15,20,-15,6,-1).
FORMULA
a(n) = binomial(2*n-4, 5) if n >= 5 else 0.
a(n) = -A053123(n,5), n >= 5; a(n) := 0, n=0..4 (sixth column of shifted Chebyshev's S-triangle, decreasing order).
G.f.: (6+20*x+6*x^2)/(1-x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6). - Harvey P. Dale, Jun 03 2013
E.g.f.: (-840 + 750*x - 330*x^2 + 95*x^3 - 20*x^4 + 4*x^5)*exp(x)/15. - G. C. Greubel, Aug 26 2018
a(n) = (2*n-8)*(2*n-7)*(2*n-6)*(2*n-5)*(2*n-4)/120. - Wesley Ivan Hurt, Mar 25 2020
From Amiram Eldar, Jan 03 2022: (Start)
Sum_{n>=5} 1/a(n) = 335/12 - 40*log(2).
Sum_{n>=5} (-1)^(n+1)/a(n) = 85/12 - 10*log(2). (End)
MATHEMATICA
Binomial[2Range[5, 40]-4, 5] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {6, 56, 252, 792, 2002, 4368}, 30] (* Harvey P. Dale, Jun 03 2013 *)
PROG
(Magma) [Binomial(2*n-4, 5): n in [5..40]]; // Vincenzo Librandi, Oct 07 2011
(Haskell)
a053127 = (* 2) . a053132 -- Reinhard Zumkeller, Mar 03 2015
(PARI) for(n=5, 50, print1(binomial(2*n-4, 5), ", ")) \\ G. C. Greubel, Aug 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved