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.

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

Offset: 0

Author

Paul D. Hanna, Mar 11 2005

Keywords

• sign

Links

• P. Barry, On the Central Coefficients of Bell Matrices, J. Int. Seq. 14 (2011) # 11.4.3, page 8.

Crossrefs

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

Programs

PARI

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

Formula

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