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Search: id:A112692
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| A112692 |
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Coefficient array of numerator polynomials of o.g.f.s (rising powers) for the columns of triangle A008517 (second-order Eulerian numbers). |
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+0
3
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| 1, 3, -1, -6, 6, -9, -70, 163, -42, -72, 30, -123, -1110, 8440, -18244, 2423, 43036, -53172, 11232, 8640, 90, -792, -7425, 137760, -771911, 1624514, 2262109, -21114844, 51074797, -54783526, 6214788, 45596664, -40513824, 7309440, 3110400, 630, -10278, -86841, 3685605, -41159454
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The sequence of row lengths is A000217 (triangular numbers): [1, 3, 6, 10, 15, 21,..].
The o.g.f. of the k-th column sequence of triangle A008517(n,k), n>=k>=1, is (2^floor(k/2))*(x^k)*p(k,x)/product((1-j*x)^(k+1-j),j=1..k), k>=2, with the row polynomials p(k,x):= sum(a(k-2,m)*x^m,m=0..(k*(k-1)/2)-1).
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LINKS
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W. Lang, First ten rows.
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EXAMPLE
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Rows: [1]; [3,-1,-6]; [6,-9,-70,163,-42,-72];...
The k=3, offset 3, column sequence [6,58,328,..] of A008517 has o.g.f. 2*(x^3)*(3-x-6*x^2)/product((1-j*x)^(4-j),j=1..3).
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CROSSREFS
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Row sums A112693. Unsigned row sums A112694.
Sequence in context: A152685 A116412 A089511 this_sequence A124929 A103407 A074475
Adjacent sequences: A112689 A112690 A112691 this_sequence A112693 A112694 A112695
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KEYWORD
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sign,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 14 2005
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