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A209776
Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section.
3
1, 3, 2, 5, 8, 4, 9, 22, 22, 8, 15, 52, 78, 56, 16, 25, 112, 226, 242, 136, 32, 41, 228, 580, 828, 692, 320, 64, 67, 446, 1374, 2456, 2726, 1872, 736, 128, 109, 848, 3074, 6612, 9158, 8336, 4864, 1664, 256, 177, 1578, 6590, 16590, 27564, 31250
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)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3....2
5....8....4
9....22...22...8
15...52...78...56...16
First three polynomials v(n,x): 1, 3 + 2x , 5 + 8x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := (x + 1)*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[%] (* A209775 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209776 *)
CROSSREFS
Sequence in context: A209757 A208932 A189951 * A019594 A085167 A127299
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 15 2012
STATUS
approved