cp's OEIS Frontend

A320902 Expansion of ogf(x, t) = u / (6*x - t*x*u - 2) with u = x*(2*x - 2*y + 8) + y - 3 and y = sqrt(1 - 4*x). Triangle read by rows: T(n, k) with 0 <= k <= n.

%I A320902 #8 Oct 25 2018 17:22:53
%S A320902 1,1,1,1,2,1,1,3,3,3,1,4,6,8,10,1,5,10,16,27,34,1,6,15,28,54,94,116,1,
%T A320902 7,21,45,95,192,329,396,1,8,28,68,155,344,688,1152,1353,1,9,36,98,240,
%U A320902 571,1260,2466,4034,4631,1,10,45,136,357,900,2135,4616,8832,14136,15895
%N A320902 Expansion of ogf(x, t) = u / (6*x - t*x*u - 2) with u = x*(2*x - 2*y + 8) + y - 3 and y = sqrt(1 - 4*x). Triangle read by rows: T(n, k) with 0 <= k <= n.
%e A320902 Triangle starts:
%e A320902 [0] [1]
%e A320902 [1] [1, 1]
%e A320902 [2] [1, 2,  1]
%e A320902 [3] [1, 3,  3,  3]
%e A320902 [4] [1, 4,  6,  8,  10]
%e A320902 [5] [1, 5, 10, 16,  27,  34]
%e A320902 [6] [1, 6, 15, 28,  54,  94,  116]
%e A320902 [7] [1, 7, 21, 45,  95, 192,  329,  396]
%e A320902 [8] [1, 8, 28, 68, 155, 344,  688, 1152, 1353]
%e A320902 [9] [1, 9, 36, 98, 240, 571, 1260, 2466, 4034, 4631]
%p A320902 X := 10: f := x -> 3/2 + (x - sqrt(1 - 4*x))*(2*x - 1)/(6*x - 2):
%p A320902 ogf := (x, t) -> f(x)/(1 - t*x*f(x)): ser := series(ogf(x, t), x, X+1):
%p A320902 row := n -> PolynomialTools:-CoefficientList(coeff(ser, x, n), t, 'termorder' = 'reverse'): ListTools:-Flatten([seq(row(n), n=0..X)]);
%Y A320902 Row sums are A320903.
%K A320902 nonn,tabl
%O A320902 0,5
%A A320902 _Peter Luschny_, Oct 23 2018