A141480 a(n) = binomial(n+2,3)*5^3.

125, 500, 1250, 2500, 4375, 7000, 10500, 15000, 20625, 27500, 35750, 45500, 56875, 70000, 85000, 102000, 121125, 142500, 166250, 192500, 221375, 253000, 287500, 325000, 365625, 409500, 456750, 507500, 561875, 620000, 682000, 748000, 818125, 892500, 971250, 1054500

Offset: 1

Author

Zerinvary Lajos, Aug 09 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Maple

seq(binomial(n+2,3)*5^3, n=1..44);

Mathematica

With[{c=5^3},c*Binomial[Range[40]+2,3]] (* Harvey P. Dale, Oct 20 2012 *)
LinearRecurrence[ {4,-6,4,-1},{125,500,1250,2500},40] (* Harvey P. Dale, Oct 20 2012 *)

Formula

G.f.: 125*x / (1-x)^4.

a(n) = C(n+2,3)*5^3, n>=1.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=125, a(2)=500, a(3)=1250, a(4)=2500. - Harvey P. Dale, Oct 20 2012

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=1} 1/a(n) = 3/250.

Sum_{n>=1} (-1)^(n+1)/a(n) = 12*log(2)/125 - 3/50. (End)

Extensions

Offset corrected by Harvey P. Dale, Oct 20 2012