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Search: id:A134565
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| A134565 |
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Expansion of reversion of (x - 2 * x^2) / (1 - x)^3. |
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+0
1
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| 1, -1, 2, -3, 7, -12, 30, -55, 143, -273, 728, -1428, 3876, -7752, 21318, -43263, 120175, -246675, 690690, -1430715, 4032015, -8414640, 23841480, -50067108, 142498692, -300830572, 859515920, -1822766520, 5225264024, -11124755664, 31983672534
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OFFSET
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1,3
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FORMULA
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Given g.f. A(x), then 1 = (1 / A(x) + 1 / A(-x)) / 2.
a(n) = -(-1)^n * binomial( n + m, n - m) / (2 * m + 1) where m = [n/2] if n>0.
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EXAMPLE
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x - x^2 + 2*x^3 - 3*x^4 + 7*x^5 - 12*x^6 + 30*x^7 - 55*x^8 + 143*x^9 + ...
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PROGRAM
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(PARI) {a(n) = local( m = n\2); if( n<1, 0, -(-1)^n * binomial( n + m, n - m) / (2 * m + 1))}
(PARI) {a(n) = if( n<1, 0, polcoeff( serreverse( (x - 2 * x^2) / (1 - x)^3 + x * O(x^n) ), n))}
(PARI) {a(n) = if( n<1, 0, polcoeff( 1 / ( 1 + 1 / serreverse( x - x^3 + x * O(x^n) )), n))}
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CROSSREFS
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-(-1)^n * A047749(n) = a(n) unless n=0. A006013(n) = a(2*n+1). - A001764(n) = a(2*n) unless n=0.
Adjacent sequences: A134562 A134563 A134564 this_sequence A134566 A134567 A134568
Sequence in context: A089324 A111759 A047749 this_sequence A100982 A034786 A080107
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Nov 01 2007
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