A114190 Expansion of 1/(1+x*(1-x)*c(-2*x)), c(x) the g.f. of A000108.

1, -1, 4, -17, 87, -490, 2945, -18517, 120340, -802005, 5451651, -37652546, 263480357, -1864065017, 13311094644, -95816113129, 694511157535, -5064818563258, 37135165923801, -273581694291309, 2024194855052180, -15034769479254861, 112062948489702251, -837936593024505298

Offset: 0

Author

Paul Barry, Nov 16 2005

Keywords

• easy
• sign

Comments

Diagonal sums of A114189. Alternating sign version of A110508.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Programs

Mathematica

CoefficientList[Series[4/(3+x+(1-x)*Sqrt[1+8*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 03 2014 *)

PARI

x='x+O('x^50); Vec(4/(3+x+(1-x)*sqrt(1+8*x))) \\ G. C. Greubel, Mar 17 2017

Formula

G.f.: 4/(3+x+(1-x)*sqrt(1+8*x)).

Conjecture: n*a(n) +(7n-10)*a(n-1) +2*(14-3n)*a(n-2) +(13n-20)*a(n-3) +(66-23n)*a(n-4) +4*(2n-7)*a(n-5)=0. - R. J. Mathar, Dec 10 2011

a(n) ~ 9 * (-1)^n * 2^(3*n+4) / (529 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 03 2014