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%I #19 Aug 12 2018 17:23:23
%S 1,3,6,15,33,60,81,189,378,675,459,1107,2349,4509,7992,2673,6588,
%T 14553,29403,55188,97416,15849,39663,90207,189351,371358,687258,
%U 1209951,95175,240894,560115,1211031,2458998,4727565,8664813,15227190,576963,1473147,3485187
%N Dziemianczuk's array S(i,j) read by antidiagonals.
%H Lars Blomberg, <a href="/A232973/b232973.txt">Table of n, a(n) for n = 0..5049</a> (The first 100 antidiagonals)
%H M. Dziemianczuk, <a href="http://paperity.org/p/34654227/counting-lattice-paths-with-four-types-of-steps">Counting Lattice Paths With Four Types of Steps</a>, Graphs and Combinatorics, September 2013, DOI 10.1007/s00373-013-1357-1.
%e Array begins:
%e 1, 3, 15, 81, 459, 2673, 15849, ...
%e 6, 33, 189, 1107, 6588, 39663, 240894, ...
%e 60, 378, 2349, 14553, 90207, 560115, 3485187, ...
%e 675, 4509, 29403, 189351, 1211031, 7715331, 49045662, ...
%e 7992, 55188, 371358, 2458998, 16112925, 104838219, 678790125, ...
%e ...
%o (PARI) \\ Dziemianczuk, Proposition 1
%o S(n,k)=sum(i=0,n+k,sum(j=0,i,binomial(k,j)*binomial(j,i-j)*binomial(2*k+n-i,k)));
%o A=[]; for(i=1,10,A=concat(A,vector(i,j,S(j-1,i-1))));
%o A \\ _Lars Blomberg_, Jul 20 2017
%Y See A122868 and A232969 for leading row row and column.
%K nonn,tabl
%O 0,2
%A _N. J. A. Sloane_, Dec 05 2013
%E a(15)-a(38) from _Lars Blomberg_, Jul 20 2017
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