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.

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, 7, 21, 45, 95, 192, 329, 396, 1, 8, 28, 68, 155, 344, 688, 1152, 1353, 1, 9, 36, 98, 240, 571, 1260, 2466, 4034, 4631, 1, 10, 45, 136, 357, 900, 2135, 4616, 8832, 14136, 15895

Offset: 0

Author

Peter Luschny, Oct 23 2018

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] [1]
[1] [1, 1]
[2] [1, 2,  1]
[3] [1, 3,  3,  3]
[4] [1, 4,  6,  8,  10]
[5] [1, 5, 10, 16,  27,  34]
[6] [1, 6, 15, 28,  54,  94,  116]
[7] [1, 7, 21, 45,  95, 192,  329,  396]
[8] [1, 8, 28, 68, 155, 344,  688, 1152, 1353]
[9] [1, 9, 36, 98, 240, 571, 1260, 2466, 4034, 4631]
		

Crossrefs

Row sums are A320903.

Programs

Maple

X := 10: f := x -> 3/2 + (x - sqrt(1 - 4*x))*(2*x - 1)/(6*x - 2):
ogf := (x, t) -> f(x)/(1 - t*x*f(x)): ser := series(ogf(x, t), x, X+1):
row := n -> PolynomialTools:-CoefficientList(coeff(ser, x, n), t, 'termorder' = 'reverse'): ListTools:-Flatten([seq(row(n), n=0..X)]);