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Search: id:A109876
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| A109876 |
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Triangle read by rows: a(n, n) = n!, and for 1 <= k < n, a(n, k) = sum_{i=0..n-1} prod_{j=i+1..i+k} f(j, n), where for x <= y, f(x, y) = x, and for x > y, f(x, y) = x-y. |
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2
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| 1, 3, 2, 6, 11, 6, 10, 24, 50, 24, 15, 45, 120, 274, 120, 21, 76, 252, 720, 1764, 720, 28, 119, 476, 1680, 5040, 13068, 5040, 36, 176, 828, 3520, 12960, 40320, 109584, 40320, 45, 249, 1350, 6750, 29880, 113400, 362880, 1026576, 362880, 55, 340, 2090, 12048
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The first four columns (excluding the initial term of each) are A000217 (triangular numbers), A006527, A062026, and A062027. The first and third diagonals are both A000142 (factorials). The second diagonal is A000254.
Without the exception for k = n, a(n, n) would be n*n! (A001563(n)). For example, a(3, 3) would be 1*2*3+2*3*1+3*1*2 instead of 1*2*3. The author's original description did not mention the exception. I guess it didn't make sense to him to add n identical terms. - David Wasserman, Oct 1 2008
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EXAMPLE
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a(5, 3) = 1*2*3 + 2*3*4 + 3*4*5 + 4*5*1 + 5*1*2 = 120.
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PROGRAM
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Contribution from David Wasserman (dwasserm(AT)earthlink.net), Oct 01 2008: (Start)
(PARI) f(x, y) = if (x > y, x - y, x);
a(n, k) = if (n == k, n!, sum (i = 0, n - 1, prod (j = i + 1, i + k, f(j, n)))); (End)
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CROSSREFS
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Cf. A109877.
Adjacent sequences: A109873 A109874 A109875 this_sequence A109877 A109878 A109879
Sequence in context: A122362 A072635 A072765 this_sequence A108284 A095011 A052616
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KEYWORD
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nonn,easy,tabl,new
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 10 2005
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EXTENSIONS
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Edited and extended. - David Wasserman (dwasserm(AT)earthlink.net), Oct 01 2008
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