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A093905
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Triangle read by rows: for 0 <= k < n, a(n, k) is the sum of the products of all subsets of {n-k, n-k+1, ..., n} with k members.
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5
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1, 1, 3, 1, 5, 11, 1, 7, 26, 50, 1, 9, 47, 154, 274, 1, 11, 74, 342, 1044, 1764, 1, 13, 107, 638, 2754, 8028, 13068, 1, 15, 146, 1066, 5944, 24552, 69264, 109584, 1, 17, 191, 1650, 11274, 60216, 241128, 663696, 1026576, 1, 19, 242, 2414, 19524, 127860
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)
Triangle A165674, which is the reversal of this triangle, is generated by the asymptotic expansion of the higher order exponential integral E(x,m=2,n).
(End)
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FORMULA
| a(n, k) = [prod_{i=n-k..n} i]*[sum_{i =n-k..n} 1/i].
a(n, k) = A067176(n, n-k-1) = A105954(k+1, n-k). Row sums are given by A093344.
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EXAMPLE
| Triangle begins:
1
1 3
1 5 11
1 7 26 50
1 9 47 154 274
...
a(5, 3) = 4*3*2+5*3*2+5*4*2+5*4*3 = 154.
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CROSSREFS
| The leading diagonal is given by A000254, Stirling numbers of first kind. The next nine diagonals are A001705, A001711, A001716, A001721, A051524, A051545, A051560, A051562 and A051564, generalized Stirling numbers.
Cf. A001705, A001711, A067176, A093344, A105954.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)
A165674 is the reversal of this triangle.
(End)
Sequence in context: A103327 A177463 A065229 * A063853 A105064 A073496
Adjacent sequences: A093902 A093903 A093904 * A093906 A093907 A093908
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2004
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EXTENSIONS
| Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2007
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