A114194 Expansion of 1/(1+x*(2-x)*c(-2*x)), c(x) the g.f. of A000108.

1, -2, 9, -46, 261, -1578, 9969, -65030, 434685, -2961922, 20497577, -143673630, 1017887989, -7277385306, 52438781409, -380442087606, 2776651758189, -20372853020466, 150186005826969, -1111840965284046, 8262492144613989, -61614023992470666, 460907701311527889

Offset: 0

Author

Paul Barry, Nov 16 2005

Keywords

• easy
• sign

Comments

Diagonal sums of A114193.

Links

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

Crossrefs

Cf. A000108, A114193.

Programs

Mathematica

CoefficientList[Series[4/(2+x-(x-2)*Sqrt[1+8*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 03 2014 *)

PARI

x='x+O('x^50); Vec(4/(2+x-(x-2)*sqrt(1+8*x))) \\ G. C. Greubel, Mar 17 2017

Formula

G.f.: 4/(2+x-(x-2)*sqrt(1+8*x)).

Conjecture: 6*(n+1)*a(n) + (37n-29)*a(n-1) + 2*(45-41n)*a(n-2) + (47n-87)*a(n-3) + 4*(5-2n)*a(n-4) = 0. - R. J. Mathar, Dec 10 2011

a(n) ~ 17 * (-1)^n * 2^(3*n+4) / (225 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 03 2014