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A208754
Triangle of coefficients of polynomials v(n,x) jointly generated with A208753; see the Formula section.
3
1, 3, 5, 2, 7, 10, 9, 28, 4, 11, 60, 28, 13, 110, 108, 8, 15, 182, 308, 72, 17, 280, 728, 352, 16, 19, 408, 1512, 1248, 176, 21, 570, 2856, 3600, 1040, 32, 23, 770, 5016, 8976, 4400, 416, 25, 1012, 8316, 20064, 14960, 2880, 64, 27, 1300, 13156, 41184
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+2x*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
7...10
9...28...4
First five polynomials v(n,x):
1
3
5 + 2x
7 + 10x
9 + 28x + 4x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*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[%] (* A208753 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208754 *)
CROSSREFS
Sequence in context: A026184 A026208 A120837 * A180077 A095749 A137988
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 03 2012
STATUS
approved