OFFSET
1,2
LINKS
Harry J. Smith, Table of n, a(n) for n=1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = n*(2n-1)*(4n-1)*(4n-3)/3.
G.f.: x*(1+65*x+155*x^2+35*x^3) / (1-x)^5. - R. J. Mathar, Oct 03 2011
From Amiram Eldar, Mar 08 2022: (Start)
Sum_{n>=1} 1/a(n) = 6*log(2) - Pi.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*sqrt(2)*log(sqrt(2)-1) - log(2) + (2*sqrt(2) - 3/2)*Pi. (End)
MATHEMATICA
Table[Binomial[4n, 4], {n, 100}] (* Wesley Ivan Hurt, Sep 27 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 70, 495, 1820, 4845}, 40] (* Harvey P. Dale, Jan 13 2015 *)
PROG
(PARI) a(n) = n*(2*n - 1)*(4*n - 1)*(4*n - 3)/3; \\ Harry J. Smith, Jul 06 2009
(Magma) [Binomial(4 n, 4): n in [1..40]]; // Vincenzo Librandi, Jan 20 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Apr 02 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Jul 06 2009
STATUS
approved