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A173622 Triangle T(n,m) read by rows: The number of m-Schroeder paths of order n with 2 diagonal steps. 2

%I #4 Mar 30 2012 17:40:17

%S 1,6,21,30,180,546,140,1430,6120,17710,630,10920,65835,245700,695640,

%T 2772,81396,690690,3322704,11515140,32212719,12012,596904,7125300,

%U 44170896,187336380,619851960,1721286532,51480,4326300,72624816

%N Triangle T(n,m) read by rows: The number of m-Schroeder paths of order n with 2 diagonal steps.

%C The case with 1 diagonal step is A060543.

%D Chunwei Song, The Generalized Schroeder Theory, El. J. Combin. 12 (2005) #R53 Theorem 2.1.

%F T(n,m) = trinomial(m*n+n-2; m*n-2,n-2,2)/(m*n-1) .

%e This is the left-lower portion of the array which starts in row n=2, columns m>=1 as:

%e 1, 2, 3, 4, 5, 6,..

%e 6, 21, 45, 78, 120, 171, 231,.. # A081266

%e 30, 180, 546, 1224, 2310, 3900, 6090, 8976,.. # bisection A055112

%e 140, 1430, 6120, 17710, 40950, 81840, 147630, 246820, 389160,.. # 5-section A034827

%e 630, 10920, 65835, 245700, 695640, 1645020, 3426885, 6497400, ...

%e 2772, 81396, 690690, 3322704, 11515140, 32212719, 77481495, ...

%e 12012, 596904, 7125300, 44170896, 187336380, 619851960, ...

%K easy,nonn,tabl

%O 2,2

%A _R. J. Mathar_, Nov 08 2010

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