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A208923
Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section.
3
1, 1, 2, 1, 6, 4, 1, 10, 14, 8, 1, 14, 32, 38, 16, 1, 18, 58, 104, 90, 32, 1, 22, 92, 222, 296, 214, 64, 1, 26, 134, 408, 738, 808, 490, 128, 1, 30, 184, 678, 1552, 2286, 2104, 1110, 256, 1, 34, 242, 1048, 2906, 5392, 6674, 5320, 2474, 512, 1, 38, 308
OFFSET
1,3
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+1)*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
1...6....4
1...10...14...8
1...14...32...38...16
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 4x^2
1 + 10x + 14x^2 + 8x^3
1 + 14x + 32x^2 + 38x^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 + 1)*u[n - 1, x] + 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[%] (* A208923 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208908 *)
CROSSREFS
Sequence in context: A293409 A051482 A349573 * A185045 A208913 A208911
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 04 2012
STATUS
approved