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A209164
Triangle of coefficients of polynomials u(n,x) jointly generated with A209165; see the Formula section.
3
1, 2, 1, 5, 5, 1, 11, 15, 6, 1, 23, 41, 27, 9, 1, 47, 105, 95, 45, 10, 1, 95, 257, 295, 185, 65, 13, 1, 191, 609, 847, 665, 315, 91, 14, 1, 383, 1409, 2303, 2177, 1295, 497, 119, 17, 1, 767, 3201, 6015, 6657, 4767, 2289, 735, 153, 18, 1, 1535, 7169, 15231
OFFSET
1,2
COMMENTS
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2....1
5....5....1
11...15...6....1
23...41...27...9...1
First three polynomials v(n,x): 1, 2 + x, 5 + 5x + x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := (x + 1)*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[%] (* A209164 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209165 *)
CROSSREFS
Sequence in context: A126350 A204111 A079502 * A209148 A126124 A123971
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 08 2012
STATUS
approved