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A048990
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Catalan numbers with even index (A000108(2*n), n >= 0): a(n) = C(4*n,2*n)/(2*n+1).
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7
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1, 2, 14, 132, 1430, 16796, 208012, 2674440, 35357670, 477638700, 6564120420, 91482563640, 1289904147324, 18367353072152, 263747951750360, 3814986502092304, 55534064877048198, 812944042149730764
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| With interpolated zeros, this is C(n)(1+(-1)^n)/2 with g.f. given by 2/(sqrt(1+4x)+sqrt(1-4x)). - Paul Barry (pbarry(AT)wit.ie), Sep 09 2004
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FORMULA
| G.f.: A(x) = sqrt(1/8*x^-1*(1-sqrt(1-16*x))).
G.f.: 2F1( (1/4, 3/4); (3/2))(16*x) [From Olivier Gerard (olivier.gerard(AT)gmail.com) Feb 17 2011]
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EXAMPLE
| sqrt(2*x^-1*(1-sqrt(1-x))) = 1 + 1/8*x + 7/128*x^2 + 33/1024*x^3 + ...
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MATHEMATICA
| f[n_] := CatalanNumber[ 2n]; Array[f, 18, 0] (* Or *)
CoefficientList[ Series[ Sqrt[2]/Sqrt[1 + Sqrt[1 - 16 x]], {x, 0, 17}], x] (* RGWv *)
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PROG
| (Mupad) combinat::dyckWords::count(2*n) $ n = 0..28 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 14 2007
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CROSSREFS
| Cf. A000108, A024492.
Equals 2 * A065097.
Cf. A000108.
Sequence in context: A155650 A168658 A146971 * A089602 A052641 A157085
Adjacent sequences: A048987 A048988 A048989 * A048991 A048992 A048993
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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