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A244489
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Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n,j)*Stirling_2(j,k)*Bell(n-j), where Bell(n) = A000110(n), for n >= 1, 0 <= k <= n-1.
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1
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1, 2, 3, 5, 10, 6, 15, 37, 31, 10, 52, 151, 160, 75, 15, 203, 674, 856, 520, 155, 21, 877, 3263, 4802, 3556, 1400, 287, 28, 4140, 17007, 28337, 24626, 11991, 3290, 490, 36, 21147, 94828, 175896, 174805, 101031, 34671, 6972, 786, 45, 115975, 562595, 1146931, 1279240, 853315, 350889, 88977, 13620, 1200, 55
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Triangle begins:
1
2 3
5 10 6
15 37 31 10
52 151 160 75 15
203 674 856 520 155 21
877 3263 4802 3556 1400 287 28
4140 17007 28337 24626 11991 3290 490 36
...
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MATHEMATICA
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T[n_, k_] := Sum[Binomial[n, j] StirlingS2[j, k] BellB[n-j], {j, k, n}];
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CROSSREFS
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Same as A049020 (which is the main entry for this triangle) except the present sequence has an extra 1 at the end of each row. - R. J. Mathar and N. J. A. Sloane, May 17 2016
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KEYWORD
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AUTHOR
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STATUS
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approved
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