A062133 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers).

0, 1, 2, 20, 36, 16, 456, 944, 672, 160, 14304, 33760, 28800, 10880, 1536, 575040, 1466752, 1413120, 666880, 157440, 14848, 27659520, 74774784, 79278080, 43330560, 13153280, 2128896, 143360, 1548126720

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• tabl
• more

Comments

The row polynomials pPL1(n,x) := Sum_{m=0..n} a(n,m)*x^m, and pPL2(n,x) := Sum_{m=0..n} A062134(n,m)*x^m appear in the k-fold convolution of the associated Pell numbers PL(n) := A001333(n+1), n >= 0, as follows: PL(k; n) := A054458(n+k,k) = (2*pPL1(k,n)*PL(n+1)+pPL2(k,n)*PL(n))/(k!*8^k), k >= 0.

Examples

			Triangle begins:
  {0};
  {1,2};
  {20,36,16};
  {456,944,672,160};
  ...
pPL1(2,n) = 4*(5+9*n+4*n^2) = 4*(1+n)*(5+4*n).
pPL2(2,n) = 8*(1+3*n+2*n^2) = 8*(1+n)*(1+2*n).
PL(2; n) = A054460(n) = (1+n)*((5+4*n)*PL(n+1)+(1+2*n)*PL(n))/16.
		

Crossrefs

Cf. A062134(n, m) (companion triangle), A054458(n, m) (convolution triangle).