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A068768
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Generalized Catalan numbers.
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1
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1, 1, 12, 150, 1944, 25992, 356832, 5008824, 71629920, 1040509152, 15315578496, 227981324736, 3426473187072, 51929043390720, 792725911280640, 12178706839758720, 188158789025809920, 2921622674591946240
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OFFSET
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0,3
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COMMENTS
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a(n)=K(6,6; n)/6 with K(a,b; n) defined in a comment to A068763.
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LINKS
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Table of n, a(n) for n=0..17.
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FORMULA
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a(n)=(6^n)*p(n, -5/6) with the row polynomials p(n, x) defined from array A068763.
a(n+1)= 6*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-24*x*(1-5*x)))/(12*x).
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CROSSREFS
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Cf. A000108, A068764-7, A068769-72, A025227-30.
Sequence in context: A154733 A056351 A056345 * A053507 A060917 A113358
Adjacent sequences: A068765 A068766 A068767 * A068769 A068770 A068771
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Mar 04, 2002
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STATUS
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approved
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