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A210193
Triangle of coefficients of polynomials u(n,x) jointly generated with A210194; see the Formula section.
3
1, 3, 6, 3, 10, 14, 3, 15, 40, 23, 3, 21, 90, 97, 32, 3, 28, 175, 301, 181, 41, 3, 36, 308, 770, 728, 292, 50, 3, 45, 504, 1722, 2346, 1452, 430, 59, 3, 55, 780, 3486, 6456, 5686, 2554, 595, 68, 3, 66, 1155, 6534, 15774, 18722, 11816, 4115, 787, 77, 3
OFFSET
1,2
COMMENTS
Row sums: powers of 3
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)+(x+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3
6....3
10...14...3
15...40...23...3
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_] := 2 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[%] (* A210193 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210194 *)
CROSSREFS
Sequence in context: A129529 A298263 A128503 * A368952 A120906 A258758
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved