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A248809
Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
1
1, 2, 1, 3, 2, 1, 8, 7, 2, 1, 15, 18, 12, 2, 1, 48, 57, 30, 18, 2, 1, 105, 174, 141, 44, 25, 2, 1, 384, 561, 414, 285, 60, 33, 2, 1, 945, 1950, 1830, 810, 510, 78, 42, 2, 1, 3840, 6555, 6090, 4680, 1410, 840, 98, 52, 2, 1, 10395, 25290, 26685, 15000, 10290
OFFSET
0,2
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + (n + 1)/f(n-1,x), where f(0,x) = 1.
(Sum of numbers in row n) = A000982(n+1) for n >= 0.
(Column 1) is essentially A006882 (double factorials).
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) = (3 + 2 x + x^2)/(2 + x), so that p(2,x) = 3 + 2 x + x^2.
First 6 rows of the triangle of coefficients:
1
2 1
3 2 1
8 7 2 1
15 18 12 2 1
48 57 30 18 2 1
MATHEMATICA
z = 15; f[x_, n_] := x + (n + 1)/f[x, n - 1]; f[x_, 0] = 1;
t = Table[Factor[f[x, n]], {n, 0, z}]
u = Numerator[t]
TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (*A248809 array*)
Flatten[CoefficientList[u, x]] (*A249809 sequence*)
PROG
(PARI) rown(n) = if (n==0, 1, x + (n+1)/rown(n-1));
tabl(nn) = for (n=0, nn, print(Vecrev(numerator(rown(n))))); \\ Michel Marcus, Oct 25 2014
CROSSREFS
Sequence in context: A107880 A102228 A141675 * A021473 A266756 A035181
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Oct 23 2014
STATUS
approved