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A210189
Triangle of coefficients of polynomials u(n,x) jointly generated with A210190; see the Formula section.
3
1, 3, 6, 2, 10, 10, 15, 30, 4, 21, 70, 28, 28, 140, 112, 8, 36, 252, 336, 72, 45, 420, 840, 360, 16, 55, 660, 1848, 1320, 176, 66, 990, 3696, 3960, 1056, 32, 78, 1430, 6864, 10296, 4576, 416, 91, 2002, 12012, 24024, 16016, 2912, 64, 105, 2730, 20020
OFFSET
1,2
COMMENTS
Column 1: triangular numbers: A000217
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x)+1,
v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3
6....2
10...10
15...30...4
First three polynomials u(n,x): 1, 3, 6 + 2x.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*u[n - 1, x] + 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[%] (* A210189 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210190 *)
CROSSREFS
Sequence in context: A354087 A210187 A364365 * A257506 A210035 A210199
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved