OFFSET
5,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 5..200
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = binomial(2*n-4, 5)/2 if n >= 5 else 0.
G.f.: (x^5)*(3+10*x+3*x^2)/(1-x)^6.
a(n) = A053127(n)/2
From Amiram Eldar, Jan 10 2022: (Start)
Sum_{n>=5} 1/a(n) = 335/6 - 80*log(2).
Sum_{n>=5} (-1)^(n+1)/a(n) = 85/6 - 20*log(2). (End)
MATHEMATICA
Binomial[2*Range[5, 40]-4, 5]/2 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {3, 28, 126, 396, 1001, 2184}, 40] (* Harvey P. Dale, Oct 25 2015 *)
PROG
(Magma) [Binomial(2*n-4, 5)/2: n in [5..40]]; // Vincenzo Librandi, Oct 07 2011
(Haskell)
a053132 n = a053132_list !! (n-5)
a053132_list = f [1] $ drop 2 a000217_list where
f xs ts'@(t:ts) = (sum $ zipWith (*) xs ts') : f (t:xs) ts
-- Reinhard Zumkeller, Mar 03 2015
(PARI) for(n=5, 50, print1(binomial(2*n-4, 5)/2, ", ")) \\ G. C. Greubel, Aug 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved