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Search: id:A067297
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| A067297 |
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Convolution of C(2,2; n) := A064340(n) (generalized Catalan numbers) with itself. |
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+0
12
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| 1, 2, 9, 64, 584, 6144, 70576, 859520, 10909440, 142773760, 1913027840, 26115182592, 361936623616, 5079287545856, 72033971859456, 1030768222437376, 14864066521333760, 215791593346695168
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n)=sum(C(2, 2; k)C(2, 2; n-k), k=0..n).
G.f.: ((3+c(4*x))/(2*(1-2*x*c(4*x))*(1+c(4*x))))^2, with c(x) g.f. for A000108 (Catalan). Also: (c(4*x)*(3+c(4*x)))^2)/(1+c(4*x))^4, or (-1+36*x +(1+24*x)*c(4*x))/((1-4*x)*(1+20*x)*c(4*x)-1+44*x-16*x^2).
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CROSSREFS
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Bisections: a(2*k)= A067320(k), a(2*k+1)= 2*A067321(k), k>=0.
Sequence in context: A052513 A024720 A094100 this_sequence A113882 A059281 A036775
Adjacent sequences: A067294 A067295 A067296 this_sequence A067298 A067299 A067300
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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 5 2002
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