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 A104506 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. 1

%I

%S 0,-1,-2,0,8,15,-6,-77,-120,117,770,946,-1728,-7735,-6930,22800,76960,

%T 42245,-282150,-751640,-125800,3341205,7145710,-2002725,-38228232,

%U -65418925,55550014,424605078,566938400,-936604097,-4587287310

%N 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.

%F 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).

%F a(n)=-sum{k=0..floor(n/2), C(n, k)C(n-k, k+1)(-1)^k} - _Paul Barry_, May 02 2005

%F E.g.f.: -exp(x)Bessel_I(1,2*I*x)/I, I=sqrt(-1); - _Paul Barry_, Feb 10 2006

%o (PARI) {a(n)=polcoeff(((1-x)/sqrt(1-2*x+5*x^2+x^2*O(x^n))-1)/(2*x),n)}

%Y Cf. A104505, A007440, A104507, A104508, A104509.

%K sign

%O 0,3

%A _Paul D. Hanna_, Mar 11 2005

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Last modified June 19 06:19 EDT 2013. Contains 226399 sequences.