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A210232
Triangle of coefficients of polynomials v(n,x) jointly generated with A210231; see the Formula section.
3
1, 2, 2, 3, 5, 3, 4, 10, 10, 4, 5, 16, 25, 18, 5, 6, 24, 48, 54, 30, 6, 7, 33, 84, 123, 106, 47, 7, 8, 44, 132, 246, 282, 194, 70, 8, 9, 56, 198, 438, 637, 594, 336, 100, 9, 10, 70, 280, 730, 1272, 1504, 1170, 556, 138, 10, 11, 85, 385, 1140, 2337, 3337, 3301
OFFSET
1,2
COMMENTS
First and last terms of row n are n.
Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
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)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...5....3
4...10...10...4
5...16...25...16...5
First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 3x^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] + 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[%] (* A210231 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210232 *)
CROSSREFS
Sequence in context: A125101 A208519 A336725 * A047666 A285935 A209568
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved