A061188 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000032(n+1), n >= 0 (Lucas numbers).

0, 1, 5, 20, 45, 25, 240, 350, 600, 250, 3000, 9250, 13125, 8750, 1875, 93000, 373750, 361875, 240625, 103125, 15625, 3690000, 11077500, 12818750, 8531250, 4156250, 1181250, 125000, 116550000, 312037500

Offset: 0

Author

Wolfdieter Lang, Apr 20 2001

Keywords

• nonn
• tabl
• more

Comments

The row polynomials pL1(n,x) := Sum_{m=0..n} a(n,m)*x^m and pL2(n,x) := Sum_{m=0..n} A061189(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:
  {0};
  {1,5};
  {20,45,25};
  {240,350,600,250};
  ...;
pL1(2,n) = 5*(4+9*n+5*n^2) = 5*(1+n)*(4+5*n).
		

Crossrefs

Cf. A061189(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).