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Search: id:A068770
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| A068770 |
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Generalized Catalan numbers. |
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+0
2
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| 1, 1, 16, 264, 4480, 77952, 1386496, 25135616, 463233024, 8658673664, 163829383168, 3132565553152, 60446638866432, 1175715287400448, 23028562592268288, 453848132868898816, 8993594212565909504
(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(8,8; n)/8 with K(a,b; n) defined in a comment to A068763.
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FORMULA
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a(n)=(8^n)*p(n, -7/8) with the row polynomials p(n, x) defined from array A068763.
a(n+1)= 8*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-32*x*(1-7*x)))/(16*x).
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CROSSREFS
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Cf. A000108, A068764-9, A068771-72, A025227-30.
Sequence in context: A067223 A041113 A041482 this_sequence A113359 A119290 A000487
Adjacent sequences: A068767 A068768 A068769 this_sequence A068771 A068772 A068773
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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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