A171215 Row cubed sums of triangle of Lucas polynomials (A034807) for n>0: Sum_{k=0..[n/2]} A034807(n,k)^3.
1, 9, 28, 73, 251, 954, 3431, 12617, 48142, 184509, 710755, 2768410, 10857575, 42779655, 169411778, 673898825, 2690398105, 10776264120, 43294049155, 174399508573, 704214759836, 2849828137869, 11555835845903, 46943852758298
Offset: 1
Keywords
Examples
L.g.f.: L(x) = x + 9*x^2/2 + 28*x^3/3 + 73*x^4/4 + 251*x^5/5 +... exp(L(x)) = 1 + x + 5*x^2 + 14*x^3 + 40*x^4 + 126*x^5 + 408*x^6 +...+ A171185(n)*x^n +...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..160
Programs
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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
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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 */
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PARI
{a(n)=sum(k=0, n\2, (binomial(n-k, k)+binomial(n-k-1, k-1))^3)}
Formula
Equals the logarithmic derivative of A171185.