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A145118
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Denominator polynomials for continued fraction generating function for n!.
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2
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1, 1, 1, -1, 1, -2, 1, -4, 2, 1, -6, 6, 1, -9, 18, -6, 1, -12, 36, -24, 1, -16, 72, -96, 24, 1, -20, 120, -240, 120, 1, -25, 200, -600, 600, -120, 1, -30, 300, -1200, 1800, -720, 1, -36, 450, -2400, 5400, -4320, 720, 1, -42, 630, -4200, 12600, -15120
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OFFSET
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0,6
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COMMENTS
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Row sums are A056920. T(n,1) gives quarter squares A002620. T(n,2) appears to coincide with 2*A000241(n+1).
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LINKS
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FORMULA
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T(n,k) = (-1)^k C(floor((n+1)/2),k) * C(floor(n/2),k)*k!.
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EXAMPLE
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Triangle begins:
1;
1;
1, -1;
1, -2;
1, -4, 2;
1, -6, 6;
1, -9, 18, -6;
1, -12, 36, -24;
1, -16, 72, -96, 24;
1, -20, 120, -240, 120;
1, -25, 200, -600, 600, -120;
1, -30, 300, -1200, 1800, -720;
1, -36, 450, -2400, 5400, -4320, 720;
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MAPLE
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T:= (n, k)-> (-1)^k* binomial(iquo(n+1, 2), k) *binomial(iquo(n, 2), k)*k!:
seq (seq (T(n, k), k=0..iquo(n, 2)), n=0..16); # Alois P. Heinz, Dec 04 2012
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CROSSREFS
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KEYWORD
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easy,sign,tabf
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AUTHOR
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STATUS
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approved
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