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A171215 Row cubed sums of triangle of Lucas polynomials (A034807) for n>0: Sum_{k=0..[n/2]} A034807(n,k)^3.

%I A171215 #12 Mar 17 2023 09:55:45
%S A171215 1,9,28,73,251,954,3431,12617,48142,184509,710755,2768410,10857575,
%T A171215 42779655,169411778,673898825,2690398105,10776264120,43294049155,
%U A171215 174399508573,704214759836,2849828137869,11555835845903,46943852758298
%N A171215 Row cubed sums of triangle of Lucas polynomials (A034807) for n>0: Sum_{k=0..[n/2]} A034807(n,k)^3.
%H A171215 Vincenzo Librandi, <a href="/A171215/b171215.txt">Table of n, a(n) for n = 1..160</a>
%F A171215 Equals the logarithmic derivative of A171185.
%e A171215 L.g.f.: L(x) = x + 9*x^2/2 + 28*x^3/3 + 73*x^4/4 + 251*x^5/5 +...
%e A171215 exp(L(x)) = 1 + x + 5*x^2 + 14*x^3 + 40*x^4 + 126*x^5 + 408*x^6 +...+ A171185(n)*x^n +...
%o A171215 (PARI) {a(n)=sum(k=0, n\2, (binomial(n-k, k)+binomial(n-k-1, k-1))^3)}
%o A171215 (Maxima) makelist(sum((binomial(n-k,k)+binomial(n-k-1, k-1))^3, k, 0, floor(n/2)), n, 1, 24); /* _Bruno Berselli_, May 19 2011 */
%o A171215 (Magma) A034807cubed:=func< n | [(Binomial(n-k,k)+Binomial(n-k-1,k-1))^3: k in [0..Floor(n/2)]] >; [&+A034807cubed(n): n in [1..24]]; // _Bruno Berselli_, May 19 2011
%Y A171215 Cf. A171185, A132461, A171187.
%K A171215 nonn
%O A171215 1,2
%A A171215 _Paul D. Hanna_, Dec 14 2009