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A209154
Triangle of coefficients of polynomials u(n,x) jointly generated with A209157; see the Formula section.
3
1, 2, 1, 4, 5, 2, 7, 14, 10, 2, 11, 32, 36, 18, 4, 16, 65, 104, 82, 32, 4, 22, 121, 258, 282, 168, 52, 8, 29, 210, 574, 820, 676, 328, 88, 8, 37, 344, 1176, 2116, 2264, 1504, 608, 136, 16, 46, 537, 2256, 4980, 6640, 5672, 3136, 1096, 224, 16, 56, 805
OFFSET
1,2
COMMENTS
Last number in each row is a power of 2.
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
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)=2x*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
4....5....2
7....14...10...2
11...32...36...18...4
First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^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] + 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[%] (* A209154 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209157 *)
CROSSREFS
Sequence in context: A145064 A209166 A209146 * A144332 A209153 A209141
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 07 2012
STATUS
approved