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A sequence related to Catalan numbers A000108.
1

%I #3 Oct 12 2012 14:40:25

%S 1,-1,1,15,113,783,5361,36879,255985,1794063,12689393,90505231,

%T 650379249,4705157135,34244198385,250572963855,1842382110705,

%U 13605619630095,100872203796465,750556607938575,5602962592235505,41952165966643215,314983352736153585

%N A sequence related to Catalan numbers A000108.

%C See also A115150, the third diagonal of triangle A113647 (called Y(2,1)).

%F (1-4*x)*(2*c(2*x)-1)/(1+x) with c(x) g.f. of A000108 (Catalan).

%F a(n)= A113647(n, n-1), n>=2.

%F a(n)= b(n)-4*b(n-1) with b(n):=A062992(n), n>=2; a(0)=1, a(1)=-1.

%e 15= a(3) = A062992(3) - 4*A062992(2) = 67 - 4*13.

%K sign,easy

%O 0,4

%A _Wolfdieter Lang_, Jan 13 2006