A161495 Expansion of x*(3*x-1)*(x-3)/(1-15*x+32*x^2-15*x^3+x^4).

3, 35, 432, 5405, 67773, 850080, 10663107, 133755235, 1677792528, 21045816925, 263993558397, 3311470367040, 41538271098243, 521045872287395, 6535871471114352, 81984366749625245, 1028391763981932093

Offset: 1

Author

R. J. Mathar, Jun 11 2009

Keywords

• nonn
• easy

Comments

Proposed by R. Guy in the seqfan list, Mar 29 2009.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..900
• Index entries for linear recurrences with constant coefficients, signature (15,-32,15,-1).

Programs

Mathematica

Rest[CoefficientList[Series[x(3x-1)(x-3)/(1-15x+32x^2-15x^3+x^4), {x,0,30}], x]] (* or *) LinearRecurrence[{15,-32,15,-1},{3,35,432,5405},30] (* Harvey P. Dale, Nov 03 2011 *)

Formula

G.f. x*(3*x-1)*(x-3)/(1-15*x+32*x^2-15*x^3+x^4).

a(n) = 15*a(n-1)-32*a(n-2)+15*a(n-3)-a(n-4).

(a(n))^2 = A161159(n)*A004254(n) = A003739(n)/(5*(A001906(n))^2).