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A174861
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A symmetrical triangular sequence:t(n,m)=n!*(StirlingS1[n, m] + StirlingS1[n, n - m] - (StirlingS1[n, 0] + StirlingS1[n, n]) + 1) - n! + 1
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0
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1, 1, 1, 1, -5, 1, 1, -11, -11, 1, 1, -311, 505, -311, 1, 1, 1561, -1919, -1919, 1561, 1, 1, -97919, 257761, -324719, 257761, -97919, 1, 1, 3517921, -8013599, 4475521, 4475521, -8013599, 3517921, 1, 1, -204382079, 539844481, -608549759, 545811841
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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, -3, -20, -115, -714, -5033, -40312, -362871, -3628790, -39916789,...}.
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LINKS
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FORMULA
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t(n,m)=n!*(StirlingS1[n, m] + StirlingS1[n, n - m] - (StirlingS1[n, 0] + StirlingS1[n, n]) + 1) - n! + 1
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EXAMPLE
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{1},
{1, 1},
{1, -5, 1},
{1, -11, -11, 1},
{1, -311, 505, -311, 1},
{1, 1561, -1919, -1919, 1561, 1},
{1, -97919, 257761, -324719, 257761, -97919, 1},
{1, 3517921, -8013599, 4475521, 4475521, -8013599, 3517921, 1},
{1, -204382079, 539844481, -608549759, 545811841, -608549759, 539844481, -204382079, 1},
{1, 14617895041, -39568072319, 41218450561, -16270087679, -16270087679, 41218450561, -39568072319, 14617895041, 1},
{1, -1316985868799, 3728392416001, -4289789548799, 2855691417601, -1954656748799, 2855691417601, -4289789548799, 3728392416001, -1316985868799, 1}
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MATHEMATICA
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t[n_, m_] = n!*(StirlingS1[n, m] + StirlingS1[n, n - m] - (StirlingS1[ n, 0] + StirlingS1[n, n]) + 1) - n! + 1;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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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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