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A209747
Triangle of coefficients of polynomials u(n,x) jointly generated with A209748; see the Formula section.
3
1, 1, 2, 3, 4, 2, 5, 10, 6, 2, 9, 20, 18, 8, 2, 15, 40, 44, 28, 10, 2, 25, 76, 102, 80, 40, 12, 2, 41, 142, 222, 210, 130, 54, 14, 2, 67, 260, 466, 512, 380, 196, 70, 16, 2, 109, 470, 948, 1188, 1022, 630, 280, 88, 18, 2, 177, 840, 1884, 2648, 2590, 1848, 980
OFFSET
1,3
COMMENTS
Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
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
1...2
3...4....2
5...10...6....2
9...20...18...8...2
First three polynomials u(n,x): 1, 1 + 2x, 3 + 4x + 2x^2.
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: A293450 A322990 A120636 * A117744 A366481 A361697
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 13 2012
STATUS
approved