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A094953
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Triangle T(n,m) read by rows: number of rises (drops) in the compositions of n with m parts, m>=2.
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5
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1, 1, 2, 2, 4, 3, 2, 8, 9, 4, 3, 12, 21, 16, 5, 3, 18, 39, 44, 25, 6, 4, 24, 66, 96, 80, 36, 7, 4, 32, 102, 184, 200, 132, 49, 8, 5, 40, 150, 320, 430, 372, 203, 64, 9, 5, 50, 210, 520, 830, 888, 637, 296, 81, 10, 6, 60, 285, 800, 1480, 1884, 1673, 1024, 414, 100, 11, 6
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OFFSET
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2,3
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LINKS
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FORMULA
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G.f. of m-th column: [(m-1)x^(m+1)]/[(1+x)(1-x)^m].
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EXAMPLE
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1
1 2
2 4 3
2 8 9 4
3 12 21 16 5
3 18 39 44 25 6
4 24 66 96 80 36 7
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MATHEMATICA
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T[n_, m_] := SeriesCoefficient[(m-1)x^(m+1)/(1+x)/(1-x)^m, {x, 0, n+1}];
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PROG
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(PARI) T(n, m)=polcoeff((m-1)*x^(m+1)/(1+x)/(1-x)^m, n)
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CROSSREFS
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Row sums are A045883, diagonals include n, n^2, (n-1)(n^2-n+2)/2, (n-1)^2(n^+n+6), etc.
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KEYWORD
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AUTHOR
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STATUS
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approved
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