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A209693
Triangle of coefficients of polynomials u(n,x) jointly generated with A209694; see the Formula section.
3
1, 0, 2, 0, 3, 3, 0, 4, 9, 4, 0, 5, 17, 19, 5, 0, 6, 27, 49, 34, 6, 0, 7, 39, 98, 115, 55, 7, 0, 8, 53, 170, 284, 236, 83, 8, 0, 9, 69, 269, 585, 706, 440, 119, 9, 0, 10, 87, 399, 1070, 1706, 1568, 763, 164, 10, 0, 11, 107, 564, 1799, 3577, 4395, 3193, 1250, 219
OFFSET
1,3
COMMENTS
Alternating row sums are periodic.
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x),
v(n,x)=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
0...2
0...2...4
0...1...8...8
0...1...5...24...16
First three polynomials v(n,x): 1, 2x, 2x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, 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[%] (* A209693 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209694 *)
CROSSREFS
Sequence in context: A127952 A171307 A372817 * A154344 A134409 A327878
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved