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A117145
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Triangle read by rows: T(n,k) is the number of partitions of n into parts of the form 2^j-1, j=1,2,... and having k parts (n>=1, k>=1). Partitions into parts of the form 2^j-1, j=1,2,... are called s-partitions.
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2
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1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1
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OFFSET
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1,39
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COMMENTS
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LINKS
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W. M. Y. Goh, P. Hitczenko and A. Shokoufandeh, s-partitions, Inform. Process. Lett., 82, 2002, 327-329.
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FORMULA
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G.f.: G(t,x) = -1+1/product(1-tx^(2^k-1), k=1..infinity).
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EXAMPLE
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T(9,3)=2 because we have [7,1,1] and [3,3,3].
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MAPLE
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g:=-1+1/product(1-t*x^(2^k-1), k=1..10): gser:=simplify(series(g, x=0, 20)): for n from 1 to 19 do P[n]:=sort(coeff(gser, x^n)) od: for n from 1 to 19 do seq(coeff(P[n], t^j), j=1..n) od; # yields sequence in triangular form
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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