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A137896
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Numerators of a rational triangle related to 1/sqrt(1-x).
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1
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 18, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 5, 100, 5, 6, 1, 1, 7, 63, 175, 175, 63, 7, 1, 1, 8, 28, 56, 490, 56, 28, 8, 1, 1, 9, 36, 84, 882, 882, 84, 36, 9, 1, 1, 10, 135, 120, 1470, 15876, 1470, 120, 135, 10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Denominators are given by A137897.
The rational triangle is the inverse of the coefficient array of the polynomial family defined
by the sequence 1/(2n+1) (reflection coefficients). The polynomials are calculated by
p(n, x):=IF(n=0, 1, x*p(n-1,x)-a(n-1)*x^(n-1)*p(n-1,1/x)) where a(n)=1/(2n+1).
The row sums of the rational triangle are the reciprocals of the expansion of 1/sqrt(1-x).
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EXAMPLE
| Triangle begins
1,
1, 1,
1, 2, 1,
1, 3, 3, 1,
1, 4, 18, 4, 1,
1, 5, 10, 10, 5, 1,
1, 6, 5, 100, 5, 6, 1,
1, 7, 63, 175, 175, 63, 7, 1,
1, 8, 28, 56, 490, 56, 28, 8, 1,
1, 9, 36, 84, 882, 882, 84, 36, 9, 1,
1, 10, 135, 120, 1470, 15876, 1470, 120, 135, 10, 1
The associated rational triangle begins
1,
1,1,
1,2/3,1,
1,3/5,3/5,1,
1,4/7,10/35,4/7,1
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CROSSREFS
| Sequence in context: A059922 A159623 A143199 * A157219 A167040 A054450
Adjacent sequences: A137893 A137894 A137895 * A137897 A137898 A137899
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KEYWORD
| frac,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 21 2008
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