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A173621 Triangle of Generalized Runyon numbers R_{n,k}^(4) read by rows.

%I A173621 #4 Mar 30 2012 17:40:17
%S A173621 1,1,4,1,12,22,1,24,120,140,1,40,380,1140,969,1,60,920,5060,10626,
%T A173621 7084,1,84,1890,16380,61425,98280,53820,1,112,3472,43400,251720,
%U A173621 704816,906192,420732,1,144,5880,99960,824670,3518592,7791168,8347680,3362260
%N A173621 Triangle of Generalized Runyon numbers R_{n,k}^(4) read by rows.
%C A173621 The Runyon numbers R_{n,k}^(1) are A001263, R_{n,k}^(2) are A108767. Row sums are in A002294.
%D A173621 Chunwei Song, The Generalized Schroeder Theory, El. J. Combin. 12 (2005) #R53
%F A173621 T(n,k) = R(n,k,4) with R(n,k,m)= binomial(n,k)*binomial(m*n,k-1)/n, 1<=k<=n.
%F A173621 T(n,n) = A002293(n).
%F A173621 T(n,n-1) = A004332(n).
%F A173621 T(n,2) = A046092(n-1).
%e A173621 The triangle starts in row n=1 as
%e A173621 1;
%e A173621 1, 4;
%e A173621 1, 12, 22;
%e A173621 1, 24, 120, 140;
%e A173621 1, 40, 380, 1140, 969;
%e A173621 1, 60, 920, 5060, 10626, 7084;
%e A173621 1, 84, 1890, 16380, 61425, 98280, 53820;
%e A173621 1, 112, 3472, 43400, 251720, 704816, 906192, 420732;
%K A173621 easy,nonn,tabl
%O A173621 1,3
%A A173621 _R. J. Mathar_, Nov 08 2010