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A093375
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Array T read by antidiagonals: T(k,n) = k*C(n+k-2,n-1).
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4
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1, 2, 1, 3, 4, 1, 4, 9, 6, 1, 5, 16, 18, 8, 1, 6, 25, 40, 30, 10, 1, 7, 36, 75, 80, 45, 12, 1, 8, 49, 126, 175, 140, 63, 14, 1, 9, 64, 196, 336, 350, 224, 84, 16, 1, 10, 81, 288, 588, 756, 630, 336, 108, 18, 1, 11, 100, 405, 960, 1470, 1512, 1050, 480, 135, 20, 1, 12
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of n-long k-ary words avoiding the pattern 1-1'2'.
T(n,n+1) = sum[i=1..n, T(n,i)].
Exponential Riordan array [(1+x)e^x, x] as a number triangle. [From Paul Barry (pbarry(AT)wit.ie), Feb 17 2009]
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LINKS
| S. Kitaev and T. Mansour, Partially ordered generalized patterns and k-ary words.
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FORMULA
| Triangle = P*M, the binomial transform of the infinite bidiagonal matrix with (1,1,1...) in the main diagonal and (1,2,3...) in the subdiagonal, extracting the zeros. P = Pascal's triangle as an infinite lower triangular matrix. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 05 2006
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EXAMPLE
| 1 1 1 1 1 1
2 4 6 8 10 12
3 9 18 30 45 63
4 16 40 80 140 224
5 25 75 175 350 630
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CROSSREFS
| Rows include A045943. Columns include A002411, A027810.
Main diagonal is A037965. Subdiagonals include A002457.
Antidiagonal sums are A001792. See A103283 for a signed version. Cf. A103406.
Sequence in context: A180378 A180383 A133807 * A103283 A104698 A067066
Adjacent sequences: A093372 A093373 A093374 * A093376 A093377 A093378
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan, Apr 28 2004
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