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A126983 Expansion of 1/(1+x*c(x)), c(x) the g.f. of Catalan numbers A000108. 9
1, -1, 0, -1, -2, -6, -18, -57, -186, -622, -2120, -7338, -25724, -91144, -325878, -1174281, -4260282, -15548694, -57048048, -210295326, -778483932, -2892818244, -10786724388, -40347919626, -151355847012, -569274150156 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Hankel transform is (-1)^n.

Catalan transform of A033999. - R. J. Mathar, Nov 11 2008

LINKS

Fung Lam, Table of n, a(n) for n = 0..1500

FORMULA

a(n) = (-1)^n*A064310(n) . a(n) = Sum_{k, 0<=k<=n} A039599(n,k)*(-2)^k.

a(n) = Sum_{k, 0<=k<=n} A106566(n,k)*(-1)^k. a(0)=1, a(n)= -A000957(n) for n>0. - Philippe Deléham, Nov 15 2009

Recurrence: 2*(n+2)*a(n+2) = (7*n+2)*a(n+1) + 2*(2*n+1)*a(n). - Fung Lam, May 07 2014

a(n) ~ -2^(2n)/sqrt(Pi*n^3)/9. - Fung Lam, May 07 2014

CROSSREFS

Sequence in context: A125306 A209797 A064310 * A104629 A000957 A125305

Adjacent sequences:  A126980 A126981 A126982 * A126984 A126985 A126986

KEYWORD

sign

AUTHOR

Philippe Deléham, Mar 21 2007

STATUS

approved

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Last modified February 24 14:41 EST 2018. Contains 299623 sequences. (Running on oeis4.)