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A086618
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Main diagonal of square table A086617 of coefficients, T(n,k), of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/[(1-x)(1-y)] + xy*f(x,y)^2.
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2
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1, 2, 7, 33, 183, 1118, 7281, 49626, 349999, 2535078, 18758265, 141254655, 1079364105, 8350678170, 65298467487, 515349097713, 4100346740511, 32858696386766, 265001681344569
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Eric Egge (eegge(AT)carleton.edu), Oct 21 2008: (Start)
a(n) is the number of permutations of length 2n which are invariant
under the reverse-complement map and have no decreasing subsequences
of length 4. (End)
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FORMULA
| a(n) = sum(k=0, n, A000108(k)*C(n, k)^2 ) where A000108(n)=Catalan(n)=(2n)!/(n!(n+1)!) and C(n, k)=n!/(k!(n-k)!). (From Michael Somos)
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EXAMPLE
| a(5)= 1118 = 1*1^2 + 1*5^2 + 2*10^2 + 5*10^2 + 14*5^2 + 42*1^2.
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CROSSREFS
| Cf. A086617 (table), A086615 (antidiagonal sums), A003046 (determinants).
Cf. A000108.
Sequence in context: A162257 A055724 A054727 * A172387 A186760 A162661
Adjacent sequences: A086615 A086616 A086617 * A086619 A086620 A086621
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003
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