A382444 - OEIS

%I #29 Sep 22 2025 16:01:36

%S 1,1,1,1,4,1,1,7,7,1,1,9,18,9,1,1,11,34,34,11,1,1,13,54,86,54,13,1,1,

%T 15,78,174,174,78,15,1,1,17,106,306,434,306,106,17,1,1,19,138,490,914,

%U 914,490,138,19,1,1,21,174,734,1710,2262,1710,734,174,21,1

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

%C Every row is symmetric.

%e Triangle begins:

%e   [0] [1]

%e   [1] [1,  1]

%e   [2] [1,  4,   1]

%e   [3] [1,  7,   7,   1]

%e   [4] [1,  9,  18,   9,   1]

%e   [5] [1, 11,  34,  34,  11,   1]

%e   [6] [1, 13,  54,  86,  54,  13,   1]

%e   [7] [1, 15,  78, 174, 174,  78,  15,   1]

%e   [8] [1, 17, 106, 306, 434, 306, 106,  17,  1]

%e   [9] [1, 19, 138, 490, 914, 914, 490, 138, 19, 1]

%e   ...

%o (SageMath)

%o y = polygen(QQ, 'y')

%o x = y.parent()[['x']].gen()

%o gf = (1 + y*x^2 + (y^2 + y)*x^3)/(1 - (1 + y)*x - y*x^2)

%o [list(u) for u in list(gf.O(11))]

%Y Similar to A008288, A103450 and A382436. Row sums are A265107.

%K nonn,tabl

%O 0,5

%A _F. Chapoton_, Mar 25 2025