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A132461
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Row squared sums of triangle of Lucas polynomials (A034807) for n>0: Sum_{k=0..[n/2]} A034807(n,k)^2, with a(0)=1.
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3
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1, 1, 5, 10, 21, 51, 122, 295, 725, 1792, 4455, 11133, 27930, 70305, 177483, 449160, 1139157, 2894625, 7367720, 18781387, 47941271, 122524216, 313484385, 802877055, 2058184346, 5280670051, 13559216117, 34841384560, 89587774395
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also equals row squared sums of triangle A132460 and so equals the sum of the initial [n/2]+1 squared terms of 1/C(x)^n where C(x) is the g.f. of the Catalan numbers (A000108).
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FORMULA
| a(n) = Sum_{k=0..[n/2]} ( C(n-k,k) + C(n-k-1,k-1) )^2 .
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PROG
| (PARI) {a(n)=sum(k=0, n\2, (binomial(n-k, k)+binomial(n-k-1, k-1))^2)} (PARI) /* squared sums of negative powers of Catalan series: */ {a(n)=local(Catalan=2/(1+sqrt(1-4*x +x*O(x^n)))); sum(k=0, n\2, polcoeff(Catalan^-n, k)^2)}
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CROSSREFS
| Cf. A034807 (Lucas polynomials); A132460, A132459; A000108 (Catalan).
Sequence in context: A001157 A002800 A132174 * A087746 A064694 A067622
Adjacent sequences: A132458 A132459 A132460 * A132462 A132463 A132464
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 21 2007
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