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A208912
Triangle of coefficients of polynomials v(n,x) jointly generated with A208911; see the Formula section.
3
1, 2, 2, 3, 5, 4, 4, 9, 15, 8, 5, 14, 36, 37, 16, 6, 20, 70, 105, 91, 32, 7, 27, 120, 235, 306, 213, 64, 8, 35, 189, 455, 791, 819, 491, 128, 9, 44, 280, 798, 1736, 2380, 2136, 1109, 256, 10, 54, 396, 1302, 3402, 5796, 6924, 5373, 2475, 512, 11, 65, 540
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...5....3
4...9....15...8
5...14...36...37...16
First five polynomials v(n,x):
1
2 + 2x
3 + 5x + 3x^2
4 + 9x + 15x^2 + 8x^3
5 + 14x + 36x^2 + 37x^3 + 16x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A208911 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208912 *)
CROSSREFS
Sequence in context: A243970 A282443 A210554 * A210212 A209762 A026408
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 03 2012
STATUS
approved