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A285935 Square array a(n, m) read by antidiagonals whose g.f. is 1 / ((1-x)^2 * (1-y)^2 - x*y).

%I A285935 #27 Jun 16 2017 22:20:55
%S A285935 1,2,2,3,5,3,4,10,10,4,5,18,26,18,5,6,30,58,58,30,6,7,47,116,153,116,
%T A285935 47,7,8,70,214,354,354,214,70,8,9,100,371,746,931,746,371,100,9,10,
%U A285935 138,612,1464,2204,2204,1464,612,138,10,11,185,969,2714,4816,5794
%N A285935 Square array a(n, m) read by antidiagonals whose g.f. is 1 / ((1-x)^2 * (1-y)^2 - x*y).
%F A285935 G.f. Sum_{n>=0, m>=0} a(n, m) * x^n * y^m = 1 / ((1-x)^2 * (1-y)^2 - x*y).
%F A285935 T(n, k) := a(n-k, k) where 0 <= k <= n.
%F A285935 a(n, m) = a(m, n) = T(n+m, n), T(n, 0) = a(n, 0) = n+1, if n>=0, m>=0.
%F A285935 Row sums are (-1)^(n+1) * A113067(n+1).
%F A285935 T(n, 1) = A177787(n+1).
%e A285935 a(n,m) 0   1   2   3
%e A285935 ----+--- --- --- ---
%e A285935 0   |  1   2   3   4
%e A285935 1   |  2   5  10  18
%e A285935 2   |  3  10  26  58
%e A285935 3   |  4  18  58 153
%t A285935 a[n_, m_] := SeriesCoefficient[1/((1-x)^2*(1-y)^2-x*y), {x, 0, n}, {y, 0, m}];
%t A285935 Table[a[n-m, m], {n, 0, 10}, {m, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 15 2017 *)
%o A285935 (PARI) {a(n, m) = if( n<0 || m<0, 0, polcoeff( polcoeff( -1/(x*y-sqr(1-x-y+x*y))*(1+x*O(x^n))*(1+y*O(y^k)), n), m))};
%Y A285935 Cf. A113067, A177787.
%K A285935 nonn,tabl
%O A285935 0,2
%A A285935 _Michael Somos_, Jun 14 2017