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A209702
Triangle of coefficients of polynomials v(n,x) jointly generated with A209701; see the Formula section.
3
1, 2, 3, 3, 5, 7, 4, 8, 16, 17, 5, 12, 30, 47, 41, 6, 17, 50, 99, 134, 99, 7, 23, 77, 181, 315, 373, 239, 8, 30, 112, 302, 628, 968, 1020, 577, 9, 38, 156, 472, 1128, 2090, 2898, 2751, 1393, 10, 47, 210, 702, 1882, 4020, 6738, 8495, 7338, 3363, 11, 57
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)+(x+1)v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...3
3...5....7
4...8....16...17
5...12...30...57...41
First three polynomials v(n,x): 1, 2 + 3x , 3 + 5x + 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];
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[%] (* A209701 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209702 *)
CROSSREFS
Sequence in context: A333295 A081493 A144680 * A077558 A122444 A373751
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved