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%I #18 Feb 05 2024 12:45:18
%S 1,105,20213,3998709,791704585,156753394977,31036379835581,
%T 6145046450172525,1216688160731724433,240898110778299543129,
%U 47696609245941810082565,9443687732585695622131557
%N a(n) = A001541(n)*A001653(n+1)*A002315(n).
%H G. C. Greubel, <a href="/A111647/b111647.txt">Table of n, a(n) for n = 0..434</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (204,-1190,204,-1).
%F 2*a(n) = A001109(3*n+1) + A001109(n+1).
%F a(n) = sqrt(A011900(2*n)*A046090(2*n)*A001109(2*n+1)).
%F a(n) = A001541(3*n) + 2*A001109(n)*A001541(n-1)*A001541(n).
%F For n>0, a(n) = A001652(3*n) - A053141(2*n)*A002315(n-1) - A001652(n-1).
%F G.f.: (1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%F 2*a(n) = A001109(n+1) + A097731(n) + 6*A097731(n-1). - _R. J. Mathar_, Jan 31 2024
%e a(1) = 105 = 3*5*7.
%t CoefficientList[Series[(1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)), {x, 0, 30}], x] (* _G. C. Greubel_, Jul 15 2018 *)
%o (PARI) x='x+O('x^30); Vec((1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1))) \\ _G. C. Greubel_, Jul 15 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)))); // _G. C. Greubel_, Jul 15 2018
%Y Cf. A001541, A001653, A002315, A111648, A111649.
%K nonn,easy
%O 0,2
%A _Charlie Marion_, Aug 24 2005
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