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%I #14 Apr 16 2024 13:51:43
%S 0,1,4,15,50,160,494,1491,4420,12925,37380,107136,304764,861445,
%T 2421700,6775755,18879734,52413856,145038890,400183575,1101277060,
%U 3023462521,8282790024,22646131200,61805595000,168399404425,458128878724,1244567262471,3376576740410,9149594423200
%N Product of Fibonacci and self-convolution of Fibonacci numbers: a(n) = A000045(n+1)*A001629(n+1).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-5,5,-1).
%F a(n) = F(n+1)*((n+2)*F(n) + (n)*F(n+2))/5 where F(n) = A000045(n) is the Fibonacci numbers.
%F G.f.: x*(1-x)/((1+x)*(1-3*x+x^2)^2).
%p a := proc(n) option remember; if n < 3 then return n^2 fi;
%p -((2 - 2*n^2 + n)*a(n - 1) + (1 - 2*n^2 + 3*n)*a(n - 2) + n^2*a(n - 3))/(n - 1)^2 end: seq(a(n), n = 0..29); # _Peter Luschny_, Apr 16 2024
%t CoefficientList[Series[x(1-x)/((1+x)*(1-3*x+x^2)^2),{x,0,29}],x] (* _Stefano Spezia_, Apr 16 2024 *)
%Y Cf. A000045, A001629.
%K nonn,easy
%O 0,3
%A _Vladimir Kruchinin_, Apr 15 2024
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