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%I #17 Sep 08 2022 08:45:44
%S 1,2,1,6,5,1,20,21,8,1,70,84,45,11,1,252,330,220,78,14,1,924,1287,
%T 1001,455,120,17,1,3432,5005,4368,2380,816,171,20,1,12870,19448,18564,
%U 11628,4845,1330,231,23,1,48620,75582,77520,54264,26334,8855,2024,300,26,1
%N Riordan array (1/sqrt(1-4x), (1-2x-(1-3x)c(x))/(x*sqrt(1-4x))), c(x) the g.f. of A000108.
%C Product of A007318 and A114422. Product of A007318^2 and A116382. Row sums are A108080.
%C Diagonal sums are A108081.
%C Riordan array (1/sqrt(1 - 4*x), x*c(x)^3) obtained from A092392 by taking every third column starting from column 0; x*c(x)^3 is the o.g.f. for A000245. - _Peter Bala_, Nov 24 2015
%H Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Barry/barry321.html">Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices</a>, Journal of Integer Sequences, 19, 2016, #16.3.5.
%F Number triangle T(n,k) = Sum_{j = 0..n} binomial(n+k,j-k)*binomialC(n,j).
%F T(n,k) = binomial(2*n + k, n + 2*k). - _Peter Bala_, Nov 24 2015
%e Triangle begins
%e 1,
%e 2, 1,
%e 6, 5, 1,
%e 20, 21, 8, 1,
%e 70, 84, 45, 11, 1,
%e 252, 330, 220, 78, 14, 1,
%e 924, 1287, 1001, 455, 120, 17, 1,
%e 3432, 5005, 4368, 2380, 816, 171, 20, 1
%o (Magma) /* As triangle */ [[Binomial(2*n+k, n+2*k): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Nov 27 2015
%Y Cf. A000245, A007318, A092392, A108080, A108081, A114422, A116382.
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Apr 28 2009
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