A185997 Inverse of 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, 2, 3, 1, 5, 11, 7, 1, 16, 48, 44, 13, 1, 64, 244, 289, 129, 21, 1, 308, 1419, 2045, 1210, 306, 31, 1, 1727, 9281, 15649, 11447, 3937, 627, 43, 1, 11008, 67236, 129112, 111890, 48586, 10680, 1156, 57, 1, 78244, 532816, 1143134, 1140554, 596698, 168102, 25293, 1969, 73, 1, 611060, 4573278, 10808122, 12163344, 7427056, 2555941, 497215, 53954, 3154, 91, 1

Offset

0,4

Links

Table of n, a(n) for n=0..65.

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

Example

Triangle begins:
  1,
  1, 1,
  2, 3, 1,
  5, 11, 7, 1,
  16, 48, 44, 13, 1,
  64, 244, 289, 129, 21, 1,
  308, 1419, 2045, 1210, 306, 31, 1,
  1727, 9281, 15649, 11447, 3937, 627, 43, 1,
  11008, 67236, 129112, 111890, 48586, 10680, 1156, 57, 1,
  78244, 532816, 1143134, 1140554, 596698, 168102, 25293, 1969, 73, 1
Production matrix 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

Crossrefs

Cf. A178121.

Inverse is A185996. First column is A185998.

Sequence in context: A178125 A147315 A085853 * A231733 A182822 A137211

Adjacent sequences: A185994 A185995 A185996 * A185998 A185999 A186000

Keyword

nonn,easy,tabl

Author

Paul Barry, Feb 08 2011

Status

approved