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A209748
Triangle of coefficients of polynomials v(n,x) jointly generated with A209747; see the Formula section.
3
1, 3, 5, 2, 9, 6, 2, 15, 16, 8, 2, 25, 36, 26, 10, 2, 41, 76, 70, 38, 12, 2, 67, 152, 172, 118, 52, 14, 2, 109, 294, 394, 328, 182, 68, 16, 2, 177, 554, 860, 840, 562, 264, 86, 18, 2, 287, 1024, 1808, 2028, 1584, 894, 366, 106, 20, 2, 465, 1864, 3692, 4676
OFFSET
1,2
COMMENTS
Alternating row sums: 1,3,3,5,5,7,7,9,9,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3
5....2
9....6....2
15...16...8...2
First three polynomials v(n,x): 1, 3, 5 + 2x.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, 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[%] (* A209747 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209748 *)
CROSSREFS
Sequence in context: A273668 A356472 A245653 * A065172 A026212 A026188
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 13 2012
STATUS
approved