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Search: id:A068766
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| A068766 |
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Generalized Catalan numbers. |
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+0
2
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| 1, 1, 8, 68, 608, 5664, 54528, 538944, 5441024, 55889408, 582348800, 6140864512, 65414742016, 702897995776, 7609805045760, 82929151328256, 908978855215104, 10014523823357952, 110840574196580352, 1231847926116384768
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=K(4,4; n)/4 with K(a,b; n) defined in a comment to A068763.
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FORMULA
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a(n)=(4^n)*p(n, -3/4) with the row polynomials p(n, x) defined from array A068763.
a(n+1)= 4*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-16*x*(1-3*x)))/(8*x).
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CROSSREFS
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Cf. A000108, A068764-5, A068767-72, A025227-30.
Adjacent sequences: A068763 A068764 A068765 this_sequence A068767 A068768 A068769
Sequence in context: A015574 A000434 A050841 this_sequence A054915 A073555 A113357
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 04, 2002
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