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

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

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