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Search: id:A126221
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| A126221 |
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a(n)=c(n)+c(n-1)+2c(n-2)+4c(n-3)+8c(n-4)+...+2^(n-2)*c(1)+2^(n-1)*c(0), where c(k) are the Catalan numbers (A000108). |
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+0
2
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| 1, 2, 5, 13, 35, 98, 286, 869, 2739, 8910, 29754, 101498, 352222, 1239332, 4410204, 15840813, 57344451, 208976022, 765945954, 2821516398, 10439890026, 38781926652, 144580149924, 540737349858, 2028319233390, 7628680720908
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OFFSET
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0,2
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COMMENT
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Row sums of A125177.
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FORMULA
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G.f.=(1-x)[1-sqrt(1-4x)]/[2x(1-2x)].
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EXAMPLE
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a(4)=35 because c(4)+c(3)+2c(2)+4c(1)+8c(0)=14+5+2*2+4*1+8*1=35.
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MAPLE
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c:=n->binomial(2*n, n)/(n+1): a:=n->c(n)+sum(2^(n-j-1)*c(j), j=0..n-1): seq(a(n), n=0..30);
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CROSSREFS
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Cf. A125177.
Sequence in context: A059027 A025198 A037247 this_sequence A107086 A089846 A131868
Adjacent sequences: A126218 A126219 A126220 this_sequence A126222 A126223 A126224
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2006
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