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A215080
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T(n,k) = Sum_{j=0..k} (k-j)^n * binomial(n,j).
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2
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1, 0, 1, 0, 1, 6, 0, 1, 11, 54, 0, 1, 20, 151, 680, 0, 1, 37, 413, 2569, 11000, 0, 1, 70, 1128, 9450, 52431, 217392, 0, 1, 135, 3104, 34416, 243255, 1251921, 5076400, 0, 1, 264, 8637, 125248, 1113027, 7025016, 34282879, 136761984, 0, 1, 521, 24327, 457807, 5064143, 38811015, 225930121, 1059812993, 4175432064, 0, 1, 1034, 69334, 1685266, 23031680, 212609518, 1465077802, 8026643702, 36519075583, 142469423360
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OFFSET
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0,6
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LINKS
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FORMULA
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T(n,k) = sum( (k-j)^n * binomial(n,j), j=0..k).
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EXAMPLE
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Triangle T(n,k) begins:
1;
0, 1;
0, 1, 6;
0, 1, 11, 54;
0, 1, 20, 151, 680;
0, 1, 37, 413, 2569, 11000;
0, 1, 70, 1128, 9450, 52431, 217392;
0, 1, 135, 3104, 34416, 243255, 1251921, 5076400;
0, 1, 264, 8637, 125248, 1113027, 7025016, 34282879, 136761984;
...
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MATHEMATICA
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Flatten[Table[Table[Sum[(k - j)^n*Binomial[n, j], {j, 0, k}], {k, 0, n}], {n, 0, 10}], 1]
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CROSSREFS
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Row sums give 215077 (binomial convolution of descending powers).
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KEYWORD
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AUTHOR
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STATUS
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approved
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