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A259546 a(n) = n^3*Fibonacci(n).

%I A259546 #23 Aug 25 2024 18:49:01
%S A259546 0,1,8,54,192,625,1728,4459,10752,24786,55000,118459,248832,511901,
%T A259546 1034488,2058750,4042752,7846061,15069888,28677479,54120000,101370906,
%U A259546 188586728,348669719,640991232,1172265625,2133603368,3866095494,6976587072,12541531081
%N A259546 a(n) = n^3*Fibonacci(n).
%H A259546 Colin Barker, <a href="/A259546/b259546.txt">Table of n, a(n) for n = 0..1000</a>
%H A259546 Prabha Sivaraman Nair and Rejikumar Karunakaran, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Nair/nair11.html">On k-Fibonacci Brousseau Sums</a>, J. Int. Seq. (2024) Art. No. 24.6.4. See p. 2.
%H A259546 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-8,5,8,-2,-4,-1).
%F A259546 G.f.: x*(x^2+1)*(x^4-4*x^3+23*x^2+4*x+1) / (x^2+x-1)^4.
%F A259546 Sum_{k=1..n} a(k) = (n^3-6*n^2+24*n-50)*A000045(n+1) + ((n+1)^3-6*(n+1)^2+24*(n+1)-50)*A000045(n) + 50. - _Prabha Sivaramannair_, Jul 15 2024
%F A259546 E.g.f.: exp(x/2)*x*(5*(1 + x)*(1 + 2*x)*cosh(sqrt(5)*x/2) + sqrt(5)*(1 + x*(9 + 4*x))*sinh(sqrt(5)*x/2))/5. - _Stefano Spezia_, Aug 25 2024
%p A259546 a:= n-> n^3*(<<1|1>, <1|0>>^n)[1, 2]:
%p A259546 seq(a(n), n=0..50);  # _Alois P. Heinz_, Jun 30 2015
%t A259546 Array[#^3*Fibonacci[#] &, 50, 0] (* _Paolo Xausa_, Jul 15 2024 *)
%o A259546 (PARI) a(n) = n^3*fibonacci(n)
%o A259546 (PARI) concat(0, Vec(x*(x^2+1)*(x^4-4*x^3+23*x^2+4*x+1)/(x^2+x-1)^4 + O(x^50)))
%Y A259546 Cf. A000045, A000578, A045925, A259451, A259547.
%K A259546 nonn,easy
%O A259546 0,3
%A A259546 _Colin Barker_, Jun 30 2015