A022997 Numerator of n*(n-2)*(2*n-1)/(2*(n-1)).

0, 15, 28, 135, 132, 455, 360, 1071, 760, 2079, 1380, 3575, 2268, 5655, 3472, 8415, 5040, 11951, 7020, 16359, 9460, 21735, 12408, 28175, 15912, 35775, 20020, 44631, 24780, 54839, 30240, 66495, 36448, 79695, 43452, 94535, 51300, 111111, 60040, 129519, 69720, 149855

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• frac

Examples

			Fractions begins with 0, 15/4, 28/3, 135/8, 132/5, 455/12, 360/7, 1071/16, 760/9, 2079/20, 1380/11, 3575/24, ...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Crossrefs

Cf. A022998 (denominators, with an offset shift).

Programs

Mathematica

a[n_] := Numerator[n*(n - 2)*(2*n - 1)/(2*(n - 1))]; Array[a, 50, 2] (* Amiram Eldar, Sep 21 2023 *)

PARI

a(n) = numerator(n*(n-2)*(2*n-1)/(2*(n-1))); \\ Amiram Eldar, Sep 21 2023

Formula

G.f.: x^3*(x^6+5x^4+20x^3+75x^2+28x+15)/((x-1)^4*(x+1)^4). - Ralf Stephan, Sep 03 2003

Sum_{n>=3} 1/a(n) = 11/9 + Pi/6 - 7*log(2)/3. - Amiram Eldar, Sep 21 2023

Extensions

More terms from Amiram Eldar, Sep 21 2023