A114191 Expansion of 1/(1+x*c(-2*x)), c(x) the g.f. of A000108.

1, -1, 3, -13, 67, -381, 2307, -14589, 95235, -636925, 4341763, -30056445, 210731011, -1493303293, 10678370307, -76957679613, 558403682307, -4075996839933, 29909606989827, -220510631755773, 1632599134961667, -12133359132082173, 90485602494971907, -676925762716041213

Offset: 0

Author

Paul Barry, Nov 16 2005

Keywords

• easy
• sign

Comments

First column of A114189. Row sums of A114193. Alternating sign version of A062992.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Programs

Mathematica

CoefficientList[Series[4/(3+Sqrt[1+8*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 12 2014 *)

Formula

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

a(n) = Sum_{k=0..n} (-2)^(n-k)*A039599(n, k) = Sum_{k=0..n} (-2)^(n-k)*C(2*n, n-k)*(2*k+1)/(n+k+1). - Philippe Deléham, Nov 17 2005

Conjecture: n*a(n) + (7*n-12)*a(n-1) + 4*(3-2*n)*a(n-2) = 0. - R. J. Mathar, Nov 14 2011

a(n) ~ (-1)^n * 2^(3*n+1) / (9 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 12 2014