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%I #10 Feb 21 2019 23:22:57
%S 1,1,3,6,18,49,155,486,1614,5414,18630,64828,228740,814485,2926323,
%T 10588486,38561814,141214570,519711666,1921126036,7129756188,
%U 26555090618,99228108222,371886366620,1397548389644,5265130603468
%N Convolution of A000108 (Catalan numbers) with A126120 (Catalan numbers interpolated with 0's).
%F G.f.: C(x)C(x^2), where C(x) = (1-sqrt(1-4x))/(2x) is the Catalan function. - _Emeric Deutsch_, Jun 22 2009
%F Conjecture: -(47*n-42)*(n+3)*(n+2)*(n+1)*a(n) + 2*(n+2)*(n+1)*(270*n^2 - 523*n + 126)*a(n-1) - 8*(n+1)*(211*n^3 - 1022*n^2 + 946*n + 63)*a(n-2) + 8*(-212*n^4 - 326*n^3 + 2489*n^2 - 1636*n + 126)*a(n-3) + 16*(985*n^4 - 8154*n^3 + 23771*n^2 - 28164*n + 11151)*a(n-4) + 32*(-386*n^4 + 5771*n^3 - 29314*n^2 + 60721*n - 43533)*a(n-5) - 64*(n-4)*(2*n-9)*(258*n^2 - 1193*n + 1267)*a(n-6) + 128*(n-5)*(2*n-9)*(2*n-11)*(82*n-203)*a(n-7) = 0. - _R. J. Mathar_, Oct 04 2014
%p C := x-> (1/2-(1/2)*sqrt(1-4*x))/x: G := C(x)*C(x^2): Gser := series(G, x = 0, 30): seq(coeff(Gser, x, n), n = 0 .. 27); # _Emeric Deutsch_, Jun 22 2009
%Y Cf. A000108, A126120.
%K nonn
%O 0,3
%A _Philippe Deléham_, Jun 02 2009
%E Extended by _Emeric Deutsch_, Jun 22 2009
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