A185996 Coefficient array of orthogonal polynomials P(n,x)=(x-2n+2)*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1, P(1,x)=x-1.

1, -1, 1, 1, -3, 1, -1, 10, -7, 1, 1, -46, 47, -13, 1, -1, 299, -373, 144, -21, 1, 1, -2577, 3606, -1696, 345, -31, 1, -1, 27636, -41746, 22374, -5605, 706, -43, 1, 1, -353404, 565202, -332934, 96359, -15086, 1295, -57, 1, -1, 5239925, -8770446, 5556536, -1790603, 327145, -35161, 2192, -73, 1, 1, -88310783, 153499519, -103128216, 36149287, -7422751, 938028, -73648, 3489, -91, 1

Offset: 0

Author

Paul Barry, Feb 08 2011

Keywords

• sign
• easy
• tabl

Examples

			Triangle begins
   1,
  -1, 1,
   1, -3, 1,
  -1, 10, -7, 1,
   1, -46, 47, -13, 1,
  -1, 299, -373, 144, -21, 1,
   1, -2577, 3606, -1696, 345, -31, 1,
  -1, 27636, -41746, 22374, -5605, 706, -43, 1,
   1, -353404, 565202, -332934, 96359, -15086, 1295, -57, 1,
  -1, 5239925, -8770446, 5556536, -1790603, 327145, -35161, 2192, -73, 1
Production matrix of inverse begins
  1, 1,
  1, 2, 1,
  0, 3, 4, 1,
  0, 0, 5, 6, 1,
  0, 0, 0, 7, 8, 1,
  0, 0, 0, 0, 9, 10, 1,
  0, 0, 0, 0, 0, 11, 12, 1,
  0, 0, 0, 0, 0, 0, 13, 14, 1,
  0, 0, 0, 0, 0, 0, 0, 15, 16, 1
		

Links

• E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Applied Mathematics, 34 (2005) pp. 101-122.

Crossrefs

Cf. A178120.

Inverse is A185997.