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A174545
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A symmetrical triangle based on Stirling numbers of the second kind :q=2;t(n,m,q)=If[m == 0 Or m == n, 1, If[Floor[n/2] greater than or equal to m, StirlingS2[ n, m]*q^m, StirlingS2[n, n - m]*q^(n - m)]]
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0
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1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 28, 2, 1, 1, 2, 60, 60, 2, 1, 1, 2, 124, 720, 124, 2, 1, 1, 2, 252, 2408, 2408, 252, 2, 1, 1, 2, 508, 7728, 27216, 7728, 508, 2, 1, 1, 2, 1020, 24200, 124320, 124320, 24200, 1020, 2, 1, 1, 2, 2044, 74640, 545680, 1360800, 545680
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OFFSET
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0,5
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COMMENTS
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Row Sums are:
{1, 2, 4, 6, 34, 126, 974, 5326, 43694, 299086, 2605534,...}
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LINKS
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FORMULA
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q=2;
t(n,m,q)=If[m == 0 Or m == n, 1, If[Floor[n/2] greater than or equal to m, StirlingS2[ n, m]*q^m, StirlingS2[n, n - m]*q^(n - m)]]
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 2, 2, 1},
{1, 2, 28, 2, 1},
{1, 2, 60, 60, 2, 1},
{1, 2, 124, 720, 124, 2, 1},
{1, 2, 252, 2408, 2408, 252, 2, 1},
{1, 2, 508, 7728, 27216, 7728, 508, 2, 1},
{1, 2, 1020, 24200, 124320, 124320, 24200, 1020, 2, 1},
{1, 2, 2044, 74640, 545680, 1360800, 545680, 74640, 2044, 2, 1}
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MATHEMATICA
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t[n_, m_, q_] = If[m == 0 || m == n, 1, If[Floor[n/2] >= m, StirlingS2[n, m]*q^ m, StirlingS2[n, n - m]*q^(n - m)]];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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