A061189 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000204(n+1), n >= 0 (Lucas numbers).

1, 2, 0, -10, 15, 25, 30, 475, 450, 125, 6000, 8500, 6250, 5000, 1250, 96000, 146250, 189375, 159375, 65625, 9375, 180000, 5355000, 8881250, 5578125, 2515625, 721875, 78125, 44100000, 254700000, 341775000

Offset: 0

Author

Wolfdieter Lang, Apr 20 2001

Keywords

• sign
• tabl
• more

Comments

The row polynomials pL2(n,x) := Sum_{m=0..n} a(n,m)*x^m and pL1(n,x) := Sum_{m=0..n} A061188(n,m)*x^m appear in the k-fold convolution of the Lucas numbers L(n+1) = A000204(n+1) = A000032(n+1), n >= 0, as follows: L(k; n) := A060922(n+k,k) = (pL1(k,n)*L(n+2)+pL2(k,n)*L(n+1))/(k!*5^k).

Examples

			Triangle begins:
  {1};
  {2,0};
  {-10,15,25};
  {30,475,450,125};
  ...;
pL2(2,n) = 5*(-2+3*n+5*n^2) = 5*(1+n)*(-2+5*n).
L(2; n) := A060922(n+2,2) = A060929(n) = (1+n)*((4+5*n)*L(n+2)+(-2+5*n)*L(n+1))/(2*5).
		

Crossrefs

Cf. A061188(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).