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A208660
Triangle of coefficients of polynomials u(n,x) jointly generated with A208904; see the Formula section.
3
1, 1, 2, 1, 8, 2, 1, 18, 14, 2, 1, 32, 52, 20, 2, 1, 50, 140, 104, 26, 2, 1, 72, 310, 380, 174, 32, 2, 1, 98, 602, 1106, 806, 262, 38, 2, 1, 128, 1064, 2744, 2924, 1472, 368, 44, 2, 1, 162, 1752, 6048, 8892, 6412, 2432, 492, 50, 2, 1, 200, 2730, 12168, 23652
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)=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....2
1...18...14...2
1...32...52...20...2
First five polynomials u(n,x):
1
1 + 2x
1 + 8x + 2x^2
1 + 18x + 14x^2 + 2x^3
1 + 32x + 52x^2 + 20x^3 + 2x^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_] := 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[%] (* A208660 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208904 *)
CROSSREFS
Sequence in context: A118961 A180956 A208921 * A367024 A114706 A046740
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 03 2012
STATUS
approved