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Search: id:A086990
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| A086990 |
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Expansion of (1+4x-sqrt(1+4x^2))/(4+6x) in powers of x. |
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+0
3
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| 0, 1, -2, 3, -4, 6, -10, 15, -20, 30, -52, 78, -96, 144, -282, 423, -420, 630, -1660, 2490, -1304, 1956, -11332, 16998, 3896, -5844, -95240, 142860, 157160, -235740, -983610, 1475415, 2634300, -3951450, -11751660, 17627490, 38381160, -57571740
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Series reversion of Sum_{k>=0} a(k)x^k is x(Sum_{k>=0} A007051(k)x^k).
G.f. A(x)=Sum_{k>=0} a(k)x^k satisfies 0=x-(4x+1)*A(x)+(3x+2)A(x)^2.
If A(x)=g.f., then y=x/A(x)-2x satisfies x^2=y^2-y.
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FORMULA
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G.f.: (1+4x-sqrt(1+4x^2))/(4+6x).
G.f.: (x-x^2*c(-x^2))/(1+x-x^2*c(-x^2)), c(x) the g.f. of A000108. - Paul Barry (pbarry(AT)wit.ie), Jun 17 2005
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PROGRAM
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(PARI) a(n)=polcoeff((1+4*x-sqrt(1+4*x^2+x*O(x^n)))/(4+6*x), n)
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CROSSREFS
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Adjacent sequences: A086987 A086988 A086989 this_sequence A086991 A086992 A086993
Sequence in context: A089223 A094861 A097699 this_sequence A090412 A073028 A104977
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jul 27 2003
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