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A090412
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A Chebyshev transform of 2^n.
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1
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1, 2, 3, 4, 6, 10, 15, 20, 30, 52, 78, 96, 144, 282, 423, 420, 630, 1660, 2490, 1304, 1956, 11332, 16998, -3896, -5844, 95240, 142860, -157160, -235740, 983610, 1475415, -2634300, -3951450, 11751660, 17627490, -38381160, -57571740, 152461740, 228692610
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: c(-x^2)/(1-2*x*c(-x^2)), c(x) g.f. of Catalan numbers A000108;
a(n)=sum(k=0..n, (k+1)*C(n, n/2-k/2)*(-1)^(n/2-k/2)*(1+(-1)^(n+k))*2^k/(n+k+2) ).
Let M = a tridiagonal matrix with 1's in the superdiagonal, [1,0,0,0,...] in the main diagonal, and [1,-1,-1,-1,...] in the subdiagonal; and V = vector [1,0,0,0,...]. The sequence is generated as a left column using iterates of M^n*V. [Gary W. Adamson, (qntmpkt(AT)yahoo.com), Jun 08 2011].
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CROSSREFS
| Cf. A086990.
Sequence in context: A173473 A097699 A086990 * A073028 A147788 A104977
Adjacent sequences: A090409 A090410 A090411 * A090413 A090414 A090415
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Dec 05 2003
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