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A209700
Triangle of coefficients of polynomials v(n,x) jointly generated with A209699; see the Formula section.
3
1, 2, 2, 3, 2, 4, 4, 2, 8, 8, 5, 2, 14, 16, 16, 6, 2, 22, 26, 40, 32, 7, 2, 32, 38, 78, 88, 64, 8, 2, 44, 52, 134, 178, 200, 128, 9, 2, 58, 68, 212, 310, 446, 440, 256, 10, 2, 74, 86, 316, 492, 846, 1042, 968, 512, 11, 2, 92, 106, 450, 732, 1452, 2062, 2462
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...2...4
4...2...8....8
5...2...14...16...16
First three polynomials v(n,x): 1, 2 + 2x , 3 + 2x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*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[%] (* A209699 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209700 *)
CROSSREFS
Sequence in context: A051693 A266470 A371745 * A115980 A088936 A328405
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved