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A114190 Expansion of 1/(1+x*(1-x)*c(-2*x)), c(x) the g.f. of A000108. 2
1, -1, 4, -17, 87, -490, 2945, -18517, 120340, -802005, 5451651, -37652546, 263480357, -1864065017, 13311094644, -95816113129, 694511157535, -5064818563258, 37135165923801, -273581694291309, 2024194855052180, -15034769479254861, 112062948489702251, -837936593024505298 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Diagonal sums of A114189. Alternating sign version of A110508.
LINKS
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
MATHEMATICA
CoefficientList[Series[4/(3+x+(1-x)*Sqrt[1+8*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 03 2014 *)
PROG
(PARI) x='x+O('x^50); Vec(4/(3+x+(1-x)*sqrt(1+8*x))) \\ G. C. Greubel, Mar 17 2017
CROSSREFS
Sequence in context: A056542 A331158 A110508 * A135168 A364212 A354308
KEYWORD
easy,sign
AUTHOR
Paul Barry, Nov 16 2005
STATUS
approved

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)