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A173622
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Triangle T(n,m) read by rows: The number of m-Schroeder paths of order n with 2 diagonal steps.
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2
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1, 6, 21, 30, 180, 546, 140, 1430, 6120, 17710, 630, 10920, 65835, 245700, 695640, 2772, 81396, 690690, 3322704, 11515140, 32212719, 12012, 596904, 7125300, 44170896, 187336380, 619851960, 1721286532, 51480, 4326300, 72624816
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OFFSET
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2,2
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COMMENTS
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The case with 1 diagonal step is A060543.
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REFERENCES
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Chunwei Song, The Generalized Schroeder Theory, El. J. Combin. 12 (2005) #R53 Theorem 2.1.
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LINKS
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FORMULA
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T(n,m) = trinomial(m*n+n-2; m*n-2,n-2,2)/(m*n-1) .
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EXAMPLE
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This is the left-lower portion of the array which starts in row n=2, columns m>=1 as:
1, 2, 3, 4, 5, 6,..
6, 21, 45, 78, 120, 171, 231,.. # A081266
30, 180, 546, 1224, 2310, 3900, 6090, 8976,.. # bisection A055112
140, 1430, 6120, 17710, 40950, 81840, 147630, 246820, 389160,.. # 5-section A034827
630, 10920, 65835, 245700, 695640, 1645020, 3426885, 6497400, ...
2772, 81396, 690690, 3322704, 11515140, 32212719, 77481495, ...
12012, 596904, 7125300, 44170896, 187336380, 619851960, ...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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