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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
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

The case with 1 diagonal step is A060543.

REFERENCES

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

LINKS

Table of n, a(n) for n=2..32.

FORMULA

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

EXAMPLE

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, ...

CROSSREFS

Sequence in context: A280296 A325407 A239920 * A302868 A064440 A106634

Adjacent sequences:  A173619 A173620 A173621 * A173623 A173624 A173625

KEYWORD

easy,nonn,tabl

AUTHOR

R. J. Mathar, Nov 08 2010

STATUS

approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)