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A114191 Expansion of 1/(1+x*c(-2*x)), c(x) the g.f. of A000108. 4
1, -1, 3, -13, 67, -381, 2307, -14589, 95235, -636925, 4341763, -30056445, 210731011, -1493303293, 10678370307, -76957679613, 558403682307, -4075996839933, 29909606989827, -220510631755773, 1632599134961667, -12133359132082173, 90485602494971907, -676925762716041213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A200754 A062992 A064062 * A107592 A215257 A295226

Adjacent sequences:  A114188 A114189 A114190 * A114192 A114193 A114194

KEYWORD

easy,sign

AUTHOR

Paul Barry, Nov 16 2005

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)