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%I #38 Apr 12 2015 10:55:54
%S 2,15,406,40258,14831678,20517694389,107429900933236,
%T 2142202276884870716,163481473873315612871890,
%U 47938888004647069685675105423,54195408755986948204810401084145420,236870277534533345162432986910962427358196
%N Number of triangular 0..1 arrays with n rows such that the k-th row of the array (with the first row of the triangle indexed with 0) has 2*k+1 elements and row sums are nondecreasing from top to bottom.
%C The number of binary strings of length a with exactly x ones (or zeros) is binomial(a, x).
%H Lars Blomberg, <a href="/A256369/b256369.txt">Table of n, a(n) for n = 1..58</a>
%F a(n) = Sum_{i_0=0..1} ... Sum_{i_k=i_(k-1)..2k+1} ... Sum_{i_(n-1)=i_(n-2)..2n-1} Product_{k=0..n-1} binomial(2k+1,i_k). - _Danny Rorabaugh_, Mar 31 2015
%e a(2) = binomial(3, 0) + binomial(3, 1)*2 + binomial(3, 2)*2 + binomial(3, 3)*2 = 15.
%e Some eligible arrays for n=2:
%e ...0......0......0......0......0......0......0......0......1......1...
%e .0.0.0..1.0.0..0.1.0..0.0.1..1.1.0..1.0.1..0.1.1..1.1.1..1.0.0..0.1.0.
%e Some eligible arrays for n=3:
%e .....0..........0..........0..........0..........0..........0.....
%e ...0.0.0......0.0.0......0.0.0......0.0.0......0.0.0......0.0.0...
%e .0.0.0.0.0..1.0.0.0.0..0.1.0.0.0..0.0.1.0.0..0.0.0.1.0..0.0.0.0.1.
%K nonn
%O 1,1
%A _Felix Fröhlich_, Mar 26 2015
%E a(4)-a(12) from _Lars Blomberg_, Apr 11 2015
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