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A133332
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Triangle read by rows giving coefficients in expansion of (1+x+x^2+...+x^(n-2))^n in powers of x.
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1
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1, 1, 3, 3, 1, 1, 4, 10, 16, 19, 16, 10, 4, 1, 1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1, 1, 6, 21, 56, 126, 246, 426, 666, 951, 1246, 1506, 1686, 1751, 1686, 1506, 1246, 951, 666, 426, 246, 126, 56, 21, 6, 1, 1, 7, 28, 84, 210, 462, 917
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OFFSET
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2,3
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LINKS
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EXAMPLE
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Triangle begins:
{1},
{1, 3, 3, 1},
{1, 4, 10, 16, 19, 16, 10, 4, 1},
{1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1},
{1, 6, 21, 56, 126, 246, 426, 666, 951, 1246, 1506, 1686, 1751, 1686, 1506,1246, 951, 666, 426, 246, 126, 56, 21, 6, 1},
...
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MAPLE
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U:=n->seriestolist(series(expand(add(x^i, i=0..n-2)^n), x, 100000));
for n from 2 to 8 do lprint(U(n)); od:
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MATHEMATICA
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f[q_, n_] = If[n == 0, 1, Sum[q^i, {i, 0, n - 1}]]; g[q_, n_] = Product[f[q, n], {m, 0, n}]; a = Table[CoefficientList[g[x, n], x], {n, 0, 10}]
Flatten[Table[Drop[CoefficientList[Expand[Total[x^Range[n]]^(n+1)], x], n+1], {n, 6}]] (* Harvey P. Dale, Feb 15 2015 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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