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A382439 Triangle read by rows: defined by the two-variable g.f. (x^3*y^2 + x^3*y - x^2*y + 1) / (1 - x^2*y - x*y - x).

%I A382439 #27 Mar 27 2025 10:02:54
%S A382439 1,1,1,1,2,1,1,5,5,1,1,7,12,7,1,1,9,24,24,9,1,1,11,40,60,40,11,1,1,13,
%T A382439 60,124,124,60,13,1,1,15,84,224,308,224,84,15,1,1,17,112,368,656,656,
%U A382439 368,112,17,1,1,19,144,564,1248,1620,1248,564,144,19,1
%N A382439 Triangle read by rows: defined by the two-variable g.f. (x^3*y^2 + x^3*y - x^2*y + 1) / (1 - x^2*y - x*y - x).
%C A382439 The alternating sum of every row n > 0 vanishes. Every row is symmetric.
%e A382439   [0] [1]
%e A382439   [1] [1,  1]
%e A382439   [2] [1,  2,   1]
%e A382439   [3] [1,  5,   5,   1]
%e A382439   [4] [1,  7,  12,   7,   1]
%e A382439   [5] [1,  9,  24,  24,   9,   1]
%e A382439   [6] [1, 11,  40,  60,  40,  11,   1]
%e A382439   [7] [1, 13,  60, 124, 124,  60,  13,   1]
%e A382439   [8] [1, 15,  84, 224, 308, 224,  84,  15,  1]
%e A382439   [9] [1, 17, 112, 368, 656, 656, 368, 112, 17, 1]
%o A382439 (Sage)
%o A382439 y = polygen(QQ, 'y')
%o A382439 x = y.parent()[['x']].gen()
%o A382439 gf = (x^3*y^2 + x^3*y - x^2*y + 1)/(1 - x^2*y - x*y - x)
%o A382439 [list(u) for u in list(gf.O(10))]
%Y A382439 Similar to A008288 and A382436. Row sums are A245990.
%K A382439 nonn,tabl
%O A382439 0,5
%A A382439 _F. Chapoton_, Mar 25 2025