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A249755
Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.
4
1, 1, 3, 1, 7, 3, 1, 12, 10, 3, 1, 18, 22, 13, 3, 1, 25, 40, 35, 16, 3, 1, 33, 65, 75, 51, 19, 3, 1, 42, 98, 140, 126, 70, 22, 3, 1, 52, 140, 238, 266, 196, 92, 25, 3, 1, 63, 192, 378, 504, 462, 288, 117, 28, 3, 1, 75, 255, 570, 882, 966, 750, 405, 145, 31
OFFSET
0,3
COMMENTS
(Sum of numbers in row n) = A000295(n+1) 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 + 7*x + 3*x^2
First 6 rows:
1
1 3
1 7 3
1 12 10 3
1 18 22 13 3
1 25 40 35 16 3
MATHEMATICA
z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + (n + 1)*x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249755 array *)
Flatten[CoefficientList[t, x]] (* A249755 sequence *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Nov 07 2014
STATUS
approved