A114194 - OEIS

%I #14 May 24 2024 15:14:22

%S 1,-2,9,-46,261,-1578,9969,-65030,434685,-2961922,20497577,-143673630,

%T 1017887989,-7277385306,52438781409,-380442087606,2776651758189,

%U -20372853020466,150186005826969,-1111840965284046,8262492144613989,-61614023992470666,460907701311527889

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

%C Diagonal sums of A114193.

%H G. C. Greubel, <a href="/A114194/b114194.txt">Table of n, a(n) for n = 0..1000</a>

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

%F 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

%F a(n) ~ 17 * (-1)^n * 2^(3*n+4) / (225 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Feb 03 2014

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

%o (PARI) x='x+O('x^50); Vec(4/(2+x-(x-2)*sqrt(1+8*x))) \\ _G. C. Greubel_, Mar 17 2017

%Y Cf. A000108, A114193.

%K easy,sign

%O 0,2

%A _Paul Barry_, Nov 16 2005