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A249130
Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
3
1, 2, 1, 2, 2, 1, 8, 6, 2, 1, 8, 16, 10, 2, 1, 48, 44, 28, 16, 2, 1, 48, 144, 104, 40, 22, 2, 1, 384, 400, 368, 232, 56, 30, 2, 1, 384, 1536, 1232, 688, 408, 72, 38, 2, 1, 3840, 4384, 5216, 3552, 1248, 708, 92, 48, 2, 1, 3840, 19200, 16704, 12096, 7632, 1968
OFFSET
0,2
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 2*floor(n/2))/f(n-1,x), where f(x,0) = 1. (Sum of numbers in row n) = A249131(n) for n >= 0. (Column 1) = A037223.
LINKS
Clark Kimberling, Rows 0..100, flattened
EXAMPLE
f(0,x) = 1/1, so that p(0,x) = 1
f(1,x) = (2 + x)/1, so that p(1,x) = 2 + x;
f(2,x) = (2 + 2 x + x^2)/(3 + x), so that p(2,x) = 2 + 2 x + x^2).
First 6 rows of the triangle of coefficients:
1
2 1
2 2 1
8 6 2 1
8 16 10 2 1
48 44 28 16 2 1
MATHEMATICA
z = 15; p[x_, n_] := x + 2 Floor[n/2]/p[x, n - 1]; p[x_, 1] = 1;
t = Table[Factor[p[x, n]], {n, 1, z}]
u = Numerator[t]
TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249130 array *)
Flatten[CoefficientList[u, x]] (* A249130 sequence *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Oct 22 2014
STATUS
approved