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Search: id:A067295
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| 14, 28, 76, 227, 715, 2333, 7810, 26663, 92456, 324700, 1152464, 4127294, 14895145, 54115895, 197764350, 726473055, 2680979820, 9934884960, 36953107320, 137913387450, 516295313430, 1938260223354
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OFFSET
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0,1
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FORMULA
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a(n)= A028364(n+3, 3) = C(0)*C(n+3)+C(1)*C(n+2)+C(2)*C(n+1)+ C(3)*C(n), with the Catalan numbers C(n)=A000108(n).
a(n)= (3*(31*n^3+163*n^2+254*n+112)/(8*(2*n+1)*(2*n+3)*(2*n+5)))*C(n+3).
G.f.: (c3(x)*c(x)-(c3(x)-1)/x)/x^3, with c3(x) := 1+x+2*x^2+5*x^3 and c(x) G.f. for Catalan numbers A000108.
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CROSSREFS
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Cf. A067294 (third column), A067296 (fifth column).
Sequence in context: A033011 A077265 A033847 this_sequence A019552 A045527 A041384
Adjacent sequences: A067292 A067293 A067294 this_sequence A067296 A067297 A067298
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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), Feb 05 2002
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