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A070031
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Expansion of (1+x*C)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
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1
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1, 4, 13, 42, 138, 462, 1573, 5434, 19006, 67184, 239666, 861764, 3120180, 11366370, 41630805, 153216570, 566343030, 2101610280, 7826451270, 29240172780, 109566326220, 411671536380, 1550629453698, 5854180360932
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = 2*(5*n+3)*binomial(2*n+1, n)/((n+2)*(n+3)) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 13 2002
a(n) = leftmost term of M^n*V, M = an infinite tridiagonal matrix with all 1's in the super and subdiagonals and all 2's in the main diagonal; with the rest zeros. V = Vector [1,2,0,0,0,...]. - Gary W. Adamson, Jun 16 2011
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CROSSREFS
| Sequence in context: A022029 A010900 A175005 * A082989 A192802 A149425
Adjacent sequences: A070028 A070029 A070030 * A070032 A070033 A070034
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2002
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