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A025748
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3rd order Patalan numbers (generalization of Catalan numbers).
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8
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1, 1, 3, 15, 90, 594, 4158, 30294, 227205, 1741905, 13586859, 107459703, 859677624, 6943550040, 56540336040, 463630755528, 3824953733106, 31724616256938, 264371802141150, 2212374554760150, 18583946259985260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| G.f. (with a(0)=0) is series reversion of x-3x^2+3x^3.
The Hankel transform of a(n) is A005130(n)3^binomial(n,2).
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LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
| G.f.: (4-(1-9x)^(1/3))/3. a(n)=3^(n-1)*2*A034000(n-1)/n!, n >= 2 and a(n)=3*A034164(n-2), n >= 2 (from wolfdieter.lang(AT)physik.uni-karlsruhe.de).
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MATHEMATICA
| CoefficientList[Series[(4-Power[1-9x, (3)^-1])/3, {x, 0, 20}], x] (* From Harvey P. Dale, Nov 14 2011 *)
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PROG
| (PARI) a(n)=if(n<1, n==0, polcoeff(serreverse(x-3*x^2+3*x^3+x*O(x^n)), n))
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CROSSREFS
| Apart from the initial 1, identical to A097188.
Sequence in context: A074550 A205576 A173695 * A097188 A201953 A185369
Adjacent sequences: A025745 A025746 A025747 * A025749 A025750 A025751
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KEYWORD
| nonn,changed
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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