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A209163
Triangle of coefficients of polynomials v(n,x) jointly generated with A209162; see the Formula section.
3
1, 2, 3, 3, 9, 5, 4, 20, 26, 11, 5, 38, 82, 71, 21, 6, 65, 204, 279, 176, 43, 7, 103, 439, 849, 845, 425, 85, 8, 154, 854, 2192, 3050, 2386, 990, 171, 9, 220, 1540, 5034, 9174, 9940, 6396, 2267, 341, 10, 303, 2616, 10578, 24232, 34102, 30228, 16521
OFFSET
1,2
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)=u(n-1,x)+(x+1)*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...9...5
4...20...26...11
5...38...82...71...21
First three polynomials v(n,x): 1, 2 + 3x, 3 + 9x + 5x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*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[%] (* A209162 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209163 *)
CROSSREFS
Sequence in context: A390375 A124931 A210226 * A124932 A248788 A340914
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 07 2012
STATUS
approved