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%I #11 Jan 22 2020 20:10:33
%S 0,1,6,43,291,1992,13595,92845,633966,4329023,29560367,201850896,
%T 1378323999,9411785201,64267689006,438847231427,2996636337771,
%U 20462312853336,139725412120339,954104794142789,6515035056168654
%N An inverse Catalan transform of J(3n)/J(3).
%C The g.f. is obtained from that of A015565 through the mapping g(x)->g(x(1-x)). A015565 may be retrieved through the mapping g(x)->g(xc(x)), where c(x) is the g.f. of A000108.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,1,-16,8).
%F G.f.: x(1-x)/(1-7x-x^2+16x^3-8x^4);
%F a(n) = 7a(n-1) + a(n-2) - 16a(n-3) + 8a(n-4);
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^k*J(3n-3k)/J(3).
%F a(n) = Sum_{k=0..n} A109466(n,k)*A015565(k). - _Philippe Deléham_, Oct 30 2008
%t LinearRecurrence[{7,1,-16,8},{0,1,6,43},30] (* _Harvey P. Dale_, Jul 19 2016 *)
%Y Cf. A001045.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Nov 17 2004
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