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A210558
Triangle of coefficients of polynomials v(n,x) jointly generated with A210557; see the Formula section.
3
1, 2, 3, 3, 7, 7, 4, 12, 20, 17, 5, 18, 40, 57, 41, 6, 25, 68, 129, 158, 99, 7, 33, 105, 243, 399, 431, 239, 8, 42, 152, 410, 824, 1200, 1160, 577, 9, 52, 210, 642, 1506, 2692, 3528, 3089, 1393, 10, 63, 280, 952, 2532, 5290, 8536, 10185, 8154, 3363, 11
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)+1,
v(n,x)=2x*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
2...3
3...7...7
4...12...20...17
5...18...40...57...41
First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 7x^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] + 1;
v[n_, x_] := 2 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[%] (* A210557 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210558 *)
CROSSREFS
Sequence in context: A171824 A143444 A108346 * A208920 A210234 A209768
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 22 2012
STATUS
approved