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A208931
Triangle of coefficients of polynomials u(n,x) jointly generated with A208932; see the Formula section.
3
1, 1, 2, 1, 8, 4, 1, 18, 20, 8, 1, 32, 64, 56, 16, 1, 50, 160, 224, 136, 32, 1, 72, 340, 680, 664, 328, 64, 1, 98, 644, 1736, 2416, 1872, 760, 128, 1, 128, 1120, 3920, 7264, 7856, 4984, 1736, 256, 1, 162, 1824, 8064, 19056, 26992, 23768, 12832, 3896
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+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
1...8....4
1...18...20...8
1...32...64...56...16
First five polynomials u(n,x):
1
1 + 2x
1 + 8x + 4x^2
1 + 18x + 20x^2 + 8x^3
1 + 32x + 64x^2 + 56x^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 + 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[%] (* A208931 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208932 *)
CROSSREFS
Sequence in context: A099379 A234014 A367994 * A133214 A191935 A156365
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 04 2012
STATUS
approved