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%I #13 Jul 21 2021 10:02:38
%S 1,1,1,5,1,1,21,6,1,1,93,25,7,1,1,421,112,29,8,1,1,1937,510,132,33,9,
%T 1,1,9017,2357,606,153,37,10,1,1,42349,11009,2819,709,175,41,11,1,1,
%U 200277,51840,13233,3324,819,198,45,12,1,1
%N Riordan array (f(x), x*g(x)), f(x) is the g.f. of A126952, g(x) is the g.f. of A117641.
%C Expansion of row sums of T_(x,3), T_(x,y) defined in A039599.
%C Matrix product P^3 * Q * P^(-3), where P denotes Pascal's triangle A007318 and Q denotes A061554 (formed from P by sorting the rows into descending order). Cf. A158793 and A158815. - _Peter Bala_, Jul 13 2021
%F Sum_{k=0..n} T(n,k)*x^k = A126952(n), A126568(n), A026375(n), A026378(n+1), A000351(n) for x = 0,1,2,3,4 respectively.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 5, 1, 1;
%e 21, 6, 1, 1;
%e 93, 25, 7, 1, 1;
%e 421, 112, 29, 8, 1, 1;
%e ...
%Y Cf. A061554, A158793, A158815, A171224.
%K nonn,tabl
%O 0,4
%A _Philippe Deléham_, Dec 06 2009
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