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%I #11 Oct 11 2022 00:50:59
%S 0,0,1,6,33,170,861,4326,21673,108450,542421,2712446,13562913,
%T 67815930,339082381,1695417366,8477097753,42385510610,211927596741,
%U 1059638071086,5298190530193,26490953000490,132454765701501,662273829905606
%N Binomial transform of a Jacobsthal convolution.
%C Binomial transform of A084152.
%H G. C. Greubel, <a href="/A084153/b084153.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-3,-10).
%F a(n) = (5^n - 2*2^n + (-1)^n)/18.
%F G.f.: x^2/((1+x)*(1-2*x)*(1-5*x)).
%F E.g.f.: exp(x)*(exp(2*x) - exp(-x))^2/18 = (exp(5*x) - 2*exp(2*x) + exp(-x))/18.
%t LinearRecurrence[{6,-3,-10}, {0,0,1}, 41] (* _G. C. Greubel_, Oct 10 2022 *)
%o (Magma) [(5^n -2^(n+1) +(-1)^n)/18: n in [0..40]]; // _G. C. Greubel_, Oct 10 2022
%o (SageMath) [(5^n -2^(n+1) +(-1)^n)/18 for n in range(41)] # _G. C. Greubel_, Oct 10 2022
%Y Cf. A084152.
%K easy,nonn
%O 0,4
%A _Paul Barry_, May 16 2003
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