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A209143
Triangle of coefficients of polynomials u(n,x) jointly generated with A209144; see the Formula section.
3
1, 2, 1, 5, 4, 11, 11, 1, 23, 28, 6, 47, 68, 23, 1, 95, 160, 74, 8, 191, 368, 216, 39, 1, 383, 832, 592, 152, 10, 767, 1856, 1552, 520, 59, 1, 1535, 4096, 3936, 1632, 270, 12, 3071, 8960, 9728, 4816, 1060, 83, 1, 6143, 19456, 23552, 13568, 3752, 436
OFFSET
1,2
COMMENTS
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,...
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)=u(n-1,x)+v(n-1,x) + 1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2....1
5....4
11...11...1
23...28...6
First three polynomials u(n,x): 1, 2 + x, 5 + 4x
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_] := 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[%] (* A209143 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209144 *)
CROSSREFS
Sequence in context: A091802 A144240 A233525 * A243274 A119914 A152192
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 06 2012
STATUS
approved