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A006632
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3*binomial(4*n-1,n-1)/(4*n-1).
(Formerly M2997)
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12
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1, 3, 15, 91, 612, 4389, 32890, 254475, 2017356, 16301164, 133767543, 1111731933, 9338434700, 79155435870, 676196049060, 5815796869995, 50318860986108, 437662920058980, 3824609516638444, 33563127932394060, 295655735395397520, 2613391671568320765
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 438
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FORMULA
| a(n) = binom[4n+3, n+1]/(4n+3) = 3 binom[4n+2, n] - binom[4n+2, n+1]. - David Callan (callan(AT)stat.wisc.edu), Sep 15 2004
G.f.: g^3 where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 11 2011
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MATHEMATICA
| InverseSeries[Series[y*(1-y)^3, {y, 0, 24}], x] (* then A(x)=y(x)/x *) - Len Smiley Apr 07 2000
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CROSSREFS
| A112385 divided by 2.
Sequence in context: A047019 A099251 A171790 * A159928 A020018 A124553
Adjacent sequences: A006629 A006630 A006631 * A006633 A006634 A006635
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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