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A210230
Triangle of coefficients of polynomials v(n,x) jointly generated with A210229; see the Formula section.
3
1, 3, 1, 6, 4, 1, 11, 11, 5, 1, 19, 26, 17, 6, 1, 32, 56, 48, 24, 7, 1, 53, 114, 121, 78, 32, 8, 1, 87, 223, 283, 223, 117, 41, 9, 1, 142, 424, 627, 584, 372, 166, 51, 10, 1, 231, 789, 1334, 1434, 1073, 579, 226, 62, 11, 1, 375, 1444, 2750, 3352, 2879, 1818
OFFSET
1,2
COMMENTS
Alternating row sums: 1,2,3,4,5,6,... (A000027)
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3....1
6....4....1
11...11...5....1
19...26...17...6...1
First three polynomials v(n,x): 1, 3 + x , 6 + 4x + x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%] (* A210229 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210230 *)
CROSSREFS
Sequence in context: A108286 A185944 A131415 * A207615 A209165 A121437
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved