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A210201
Triangle of coefficients of polynomials u(n,x) jointly generated with A210202; see the Formula section.
3
1, 3, 6, 3, 11, 10, 6, 19, 27, 23, 12, 32, 62, 73, 52, 24, 53, 132, 193, 187, 116, 48, 87, 266, 468, 552, 462, 256, 96, 142, 517, 1061, 1482, 1495, 1112, 560, 192, 231, 978, 2297, 3688, 4369, 3896, 2624, 1216, 384, 375, 1813, 4797, 8703, 11758
OFFSET
1,2
COMMENTS
Row sums: 3^(n-1)
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)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3
6....3
11...10...6
19...27...23...12
First three polynomials u(n,x): 1, 3, 6 + 3x.
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_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A210201 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210202 *)
CROSSREFS
Sequence in context: A368952 A120906 A258758 * A275535 A160899 A360981
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved