A030280 COMPOSE triangular numbers with triangular numbers.

1, 6, 30, 137, 588, 2415, 9600, 37209, 141336, 528049, 1945800, 7086555, 25550547, 91319973, 323890062, 1140985116, 3995155506, 13913280006, 48216776266, 166355744244, 571636515369, 1957015021744, 6677155551312

Offset: 1

Author

Christian G. Bower

Keywords

• nonn
• nice
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane, Transforms
• Index entries for linear recurrences with constant coefficients, signature (12, -57, 139, -195, 174, -102, 39, -9, 1).

Programs

Mathematica

CoefficientList[Series[((1-x)^6)/((1-4x+3x^2-x^3)^3),{x,0,30}],x] (* or *) LinearRecurrence[{12,-57,139,-195,174,-102,39,-9,1},{1,6,30,137,588,2415,9600,37209,141336},30] (* Harvey P. Dale, Jan 08 2013 *)

Formula

G.f.: [(1-x)^6]/[(1-4x+3x^2-x^3)^3].

a(1)=1, a(2)=6, a(3)=30, a(4)=137, a(5)=588, a(6)=2415, a(7)=9600, a(8)=37209, a(9)=141336, a(n)=12*a(n-1)-57*a(n-2)+139*a(n-3)- 195*a(n-4)+ 174*a(n-5)-102*a(n-6)+39*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jan 08 2013