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A053127 Binomial coefficients C(2*n-4,5). 7
6, 56, 252, 792, 2002, 4368, 8568, 15504, 26334, 42504, 65780, 98280, 142506, 201376, 278256, 376992, 501942, 658008, 850668, 1086008, 1370754, 1712304, 2118760, 2598960, 3162510, 3819816, 4582116, 5461512, 6471002, 7624512 (list; graph; refs; listen; history; text; internal format)
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 sequences related to Chebyshev polynomials.

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

Cf. A053123, A053132, A053126.

Sequence in context: A137034 A177059 A345473 * A068495 A166766 A221401

Adjacent sequences:  A053124 A053125 A053126 * A053128 A053129 A053130

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified July 7 02:44 EDT 2022. Contains 355141 sequences. (Running on oeis4.)