cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A178121 Inverse of coefficient array of orthogonal polynomials P(n,x)=(x-2n)*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1,P(1,x)=x-2.

Original entry on oeis.org

1, 2, 1, 5, 6, 1, 16, 32, 12, 1, 64, 180, 109, 20, 1, 308, 1111, 934, 276, 30, 1, 1727, 7554, 8095, 3352, 585, 42, 1, 11008, 56228, 72884, 39006, 9580, 1100, 56, 1, 78244, 454572, 688562, 451992, 144706, 23396, 1897, 72, 1, 611060, 3962218, 6845904, 5317440
Offset: 0

Views

Author

Paul Barry, May 20 2010

Keywords

Comments

Inverse is A178120. First column is A178119.

Examples

			Triangle begins
1,
2, 1,
5, 6, 1,
16, 32, 12, 1,
64, 180, 109, 20, 1,
308, 1111, 934, 276, 30, 1,
1727, 7554, 8095, 3352, 585, 42, 1,
11008, 56228, 72884, 39006, 9580, 1100, 56, 1,
78244, 454572, 688562, 451992, 144706, 23396, 1897, 72, 1
Production matrix is
2, 1,
1, 4, 1,
0, 3, 6, 1,
0, 0, 5, 8, 1,
0, 0, 0, 7, 10, 1,
0, 0, 0, 0, 9, 12, 1,
0, 0, 0, 0, 0, 11, 14, 1,
0, 0, 0, 0, 0, 0, 13, 16, 1,
0, 0, 0, 0, 0, 0, 0, 15, 18, 1

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.

Original entry on oeis.org

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

Views

Author

Paul Barry, Feb 08 2011

Keywords

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.
Showing 1-2 of 2 results.

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