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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Applied Mathematics, 34 (2005) pp. 101-122.
EXAMPLE
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
CROSSREFS
Cf. A178120.
Inverse is A185997.
Sequence in context: A263864 A060543 A267751 * A261215 A176157 A176156
KEYWORD
sign,easy,tabl
AUTHOR
Paul Barry, Feb 08 2011
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)