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A104506
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Column 1 of triangle A104505, which is equal to the right-hand side of the triangle A084610 of coefficients in (1 + x - x^2)^n.
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1
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0, -1, -2, 0, 8, 15, -6, -77, -120, 117, 770, 946, -1728, -7735, -6930, 22800, 76960, 42245, -282150, -751640, -125800, 3341205, 7145710, -2002725, -38228232, -65418925, 55550014, 424605078, 566938400, -936604097, -4587287310
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: ((1-x)/sqrt(1-2*x+5*x^2) - 1)/(2*x).
a(n) = (-1)^n*n*A007440(n) (reversion of g.f. for Fibonacci numbers).
a(n) = -Sum_{k=0..floor(n/2)} C(n, k)*C(n-k, k+1)*(-1)^k. - Paul Barry, May 02 2005
E.g.f.: -exp(x)Bessel_I(1,2*i*x)/i, i=sqrt(-1). - Paul Barry, Feb 10 2006
-(n-1)*(n+1)*a(n) + n*(2*n-1)*a(n-1) - 5*n*(n-1)*a(n-2) = 0. - R. J. Mathar, Aug 17 2017
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PROG
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(PARI) {a(n)=polcoeff(((1-x)/sqrt(1-2*x+5*x^2+x^2*O(x^n))-1)/(2*x), n)}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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