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%I #11 Feb 25 2026 21:01:50
%S 1,3,8,21,56,150,400,1065,2840,7578,20208,53874,143664,383148,1021728,
%T 2724465,7265240,19374450,51665200,137772246,367392656,979719348,
%U 2612584928,6966873546,18578329456,49542281220,132112749920
%N A Chebyshev transform of 3^n.
%H Max Alekseyev, <a href="https://mathoverflow.net/a/468699">Recursion for the Chebyshev transform of m^n</a>, answer to question on MathOverflow, 2024.
%F G.f.: c(-x^2)/(1-3xc(-x^2)), c(x) g.f. of Catalan numbers A000108; a(n)=sum{k=0..n, (k+1)C(n, n/2-k/2)(-1)^(n/2-k/2)(1+(-1)^(n+k))3^k/(n+k+2)}.
%F Conjecture: 3*(n+1)*a(n) -8*(n+1)*a(n-1) +12*(n-2)*a(n-2) +32*(2-n)*a(n-3)=0. - _R. J. Mathar_, Sep 27 2012
%K easy,nonn
%O 0,2
%A _Paul Barry_, Dec 05 2003