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A068771
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Generalized Catalan numbers.
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3
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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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LINKS
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Fung Lam, Table of n, a(n) for n = 0..725
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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).
Recurrence: (n+1)*a(n) = 288*(2-n)*a(n-2) + 18*(2*n-1)*a(n-1). - Fung Lam, Mar 04 2014
a(n) ~ sqrt(2) * 24^n / (3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 04 2014
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MATHEMATICA
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a[n_] := (288 (2 - n) a[n - 2] + 18 (2 n - 1) a[n - 1])/(n + 1); Table[a[n], {n, 0, 20}](* Wesley Ivan Hurt, Mar 04 2014 *)
CoefficientList[Series[(1-Sqrt[1-36*x*(1-8*x)])/(18*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 04 2014 *)
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CROSSREFS
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Cf. A000108, A068764-A068770, A068772, A025227-A025230.
Sequence in context: A222812 A166787 A280806 * A039646 A212669 A158590
Adjacent sequences: A068768 A068769 A068770 * 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, Mar 04 2002
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STATUS
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approved
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