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A155452
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Triangle read by rows: let t1(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]; then T(n,m)=2*t1(n + 1, k) - (m! - n! + (-m + n)!).
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0
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1, 1, 1, 1, 8, 1, 1, 25, 25, 1, 1, 69, 152, 69, 1, 1, 209, 716, 716, 209, 1, 1, 839, 3076, 5540, 3076, 839, 1, 1, 4813, 13504, 36248, 36248, 13504, 4813, 1, 1, 36283, 68814, 216662, 352652, 216662, 68814, 36283, 1, 1, 324585, 453518, 1272538, 2983444
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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, 10, 52, 292, 1852, 13372, 109132, 996172, 10068172, 111674572,...}.
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LINKS
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EXAMPLE
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{1},
{1, 1},
{1, 8, 1},
{1, 25, 25, 1},
{1, 69, 152, 69, 1},
{1, 209, 716, 716, 209, 1},
{1, 839, 3076, 5540, 3076, 839, 1},
{1, 4813, 13504, 36248, 36248, 13504, 4813, 1},
{1, 36283, 68814, 216662, 352652, 216662, 68814, 36283, 1},
{1, 324585, 453518, 1272538, 2983444, 2983444, 1272538, 453518, 324585, 1},
{1, 3269991, 3893752, 8030730, 23104284, 35077056, 23104284, 8030730, 3893752, 3269991, 1}
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MATHEMATICA
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t[n_, k_] = Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];
Table[Table[(2*t[n + 1, k] - (k! - n! + (-k + n)!)), {k, 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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EXTENSIONS
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STATUS
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approved
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