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A210682
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Triangle read by rows: T(n,k) = coefficient of x^k in polynomial U_n(x) defined by U_1 = x, U_n = n*x^n + (1-x^n)*U_(n-1), n >= 1, 1 <= k <= n(n+1)/2.
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1
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1, 1, 2, -1, 1, 2, 2, -1, -2, 1, 1, 2, 2, 3, -3, -1, -2, 1, 2, -1, 1, 2, 2, 3, 2, -2, -4, -1, -1, 2, 1, 2, -1, -2, 1, 1, 2, 2, 3, 2, 4, -5, -3, -3, -1, -1, 4, 3, -1, 2, -2, -1, -2, 1, 2, -1, 1, 2, 2, 3, 2, 4, 2, -4, -5, -3, -4, 2, -1, 4, 5, 1, 0, -1, -3, -1, 0
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OFFSET
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1,3
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COMMENTS
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T(n,m) = d(m) for m <= n (cf. A000005).
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LINKS
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EXAMPLE
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Triangle begins:
1
1 2 -1
1 2 2 -1 -2 1
1 2 2 3 -3 -1 -2 1 2 -1
...
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MAPLE
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U:= proc(n) U(n):= `if`(n=1, x, expand (n*x^n + (1-x^n)*U(n-1))) end:
T:= (n, k)-> coeff (U(n), x, k):
seq(seq(T(n, k), k=1..n*(n+1)/2), n=1..10); # Alois P. Heinz, May 30 2012
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MATHEMATICA
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U[1] = x; U[n_] := U[n] = n*x^n + (1-x^n)*U[n-1]; T[n_, k_] := Coefficient[U[n], x, k]; Table[T[n, k], {n, 1, 10}, {k, 1, n*(n+1)/2}] // Flatten (* Jean-François Alcover, Mar 07 2014 *)
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CROSSREFS
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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