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A249757
Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + 2*n*x, p(0,x) = 1.
2
1, 1, 3, 1, 8, 3, 1, 15, 11, 3, 1, 24, 26, 14, 3, 1, 35, 50, 40, 17, 3, 1, 48, 85, 90, 57, 20, 3, 1, 63, 133, 175, 147, 77, 23, 3, 1, 80, 196, 308, 322, 224, 100, 26, 3, 1, 99, 276, 504, 630, 546, 324, 126, 29, 3, 1, 120, 375, 780, 1134, 1176, 870, 450, 155
OFFSET
0,3
COMMENTS
(Sum of numbers in row n) = A097809(n) for n >= 0.
LINKS
Clark Kimberling, Rows n = 0..100, flattened
EXAMPLE
p(0,x) = 1
p(1,x) = 1 + 3*x
p(2,x) = 1 + 8*x + 3*x^2
First 6 rows:
1
1 3
1 8 3
1 15 11 3
1 24 26 14 3
1 35 50 40 17 3
MATHEMATICA
z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + 2*n*x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249757 array *)
Flatten[CoefficientList[t, x]] (* A249757 sequence *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Nov 07 2014
STATUS
approved