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Search: id:A068771
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| A068771 |
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Generalized Catalan numbers. |
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+0
2
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| 1, 1, 18, 333, 6318, 122634, 2429028, 48974949, 1002875094, 20814628158, 437088964860, 9272342710962, 198456435657036, 4280758166952756, 92972201833888200, 2031520673763657621, 44630859892110807654
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OFFSET
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0,3
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FORMULA
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a(n)=(9^n)*p(n, -8/9) with the row polynomials p(n, x) defined from array A068763.
a(n+1)= 9*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-36*x*(1-8*x)))/(18*x).
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CROSSREFS
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Cf. A000108, A068764-70, A068772-72, A025227-30.
Sequence in context: A001027 A041145 A041614 this_sequence A039646 A127585 A086502
Adjacent sequences: A068768 A068769 A068770 this_sequence A068772 A068773 A068774
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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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