This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173622 #4 Mar 30 2012 17:40:17 %S A173622 1,6,21,30,180,546,140,1430,6120,17710,630,10920,65835,245700,695640, %T A173622 2772,81396,690690,3322704,11515140,32212719,12012,596904,7125300, %U A173622 44170896,187336380,619851960,1721286532,51480,4326300,72624816 %N A173622 Triangle T(n,m) read by rows: The number of m-Schroeder paths of order n with 2 diagonal steps. %C A173622 The case with 1 diagonal step is A060543. %D A173622 Chunwei Song, The Generalized Schroeder Theory, El. J. Combin. 12 (2005) #R53 Theorem 2.1. %F A173622 T(n,m) = trinomial(m*n+n-2; m*n-2,n-2,2)/(m*n-1) . %e A173622 This is the left-lower portion of the array which starts in row n=2, columns m>=1 as: %e A173622 1, 2, 3, 4, 5, 6,.. %e A173622 6, 21, 45, 78, 120, 171, 231,.. # A081266 %e A173622 30, 180, 546, 1224, 2310, 3900, 6090, 8976,.. # bisection A055112 %e A173622 140, 1430, 6120, 17710, 40950, 81840, 147630, 246820, 389160,.. # 5-section A034827 %e A173622 630, 10920, 65835, 245700, 695640, 1645020, 3426885, 6497400, ... %e A173622 2772, 81396, 690690, 3322704, 11515140, 32212719, 77481495, ... %e A173622 12012, 596904, 7125300, 44170896, 187336380, 619851960, ... %K A173622 easy,nonn,tabl %O A173622 2,2 %A A173622 _R. J. Mathar_, Nov 08 2010