A068180 (Product_{i=1..4} (x+i)) / (Product_{i=1..4} (x-i)) = Sum_{n>=1} a(n)/A067419(n)*x^n.

1, 25, 625, 11095, 164125, 2201575, 28021525, 346791295, 4228592125, 51161968375, 616523997925, 7414045240495, 89064205082125, 1069348964379175, 12835676881182325, 154049132081273695

Offset: 1

Author

Benoit Cloitre, Mar 12 2002

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..900
• Index entries for linear recurrences with constant coefficients, signature (25,-210,720,-864).

Crossrefs

Cf. A067419.

Programs

Mathematica

LinearRecurrence[{25,-210,720,-864},{1,25,625,11095,164125},30] (* Harvey P. Dale, Oct 28 2015 *)

Formula

Lim_{n->infinity} a(n)/A067419(n) = 20.

For n > 1, a(n) = (5/6)*12^n - (15/2)*6^n + (35/2)*4^n - (35/3)*3^n. - Ralf Stephan, May 08 2004

G.f.: x*(864*x^4 + 210*x^2 + 1) / ((3*x-1)*(4*x-1)*(6*x-1)*(12*x-1)). - Colin Barker, Jun 17 2013