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A000782
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2*Catalan(n)-Catalan(n-1).
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3
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1, 3, 8, 23, 70, 222, 726, 2431, 8294, 28730, 100776, 357238, 1277788, 4605980, 16715250, 61020495, 223931910, 825632610, 3056887680, 11360977650, 42368413620, 158498860260, 594636663660, 2236748680998, 8433988655580, 31872759742852, 120699748759856
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = (7n-5)/(n+1) * C(n-1), where C(n) = A000108(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 13 2004
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REFERENCES
| J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups. Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
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FORMULA
| Expansion of (1+x^1*C^1)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
Also, apart from initial term, expansion of (1+x^2*C^2)*C, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
a(n) = leftmost column term of M^(n-1)*V, where M = a tridiagonal matrix with 1's in the super and subdiagonals, (1,2,2,2,...) in the main diagonal; and the rest zeros. V = the vector [1,2,0,0,0,...].
- Gary W. Adamson, Jun 16 2011
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CROSSREFS
| Partial sums of A071735. Cf. A000108.
Essentially the same as A061557.
Sequence in context: A005960 A184120 A061557 * A148775 A148776 A127385
Adjacent sequences: A000779 A000780 A000781 * A000783 A000784 A000785
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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