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A210200
Triangle of coefficients of polynomials v(n,x) jointly generated with A210199; see the Formula section.
3
1, 2, 2, 4, 5, 2, 7, 12, 7, 2, 12, 25, 21, 9, 2, 20, 50, 53, 32, 11, 2, 33, 96, 124, 94, 45, 13, 2, 54, 180, 273, 250, 150, 60, 15, 2, 88, 331, 577, 617, 445, 223, 77, 17, 2, 143, 600, 1181, 1444, 1212, 728, 315, 96, 19, 2, 232, 1075, 2358, 3242, 3101, 2163
OFFSET
1,2
COMMENTS
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)=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
4....5....2
7....12...7....2
12...25...21...9...2
First three polynomials v(n,x): 1, 2 + 2x , 4 + 5x + 2x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, 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[%] (* A210199 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210200 *)
CROSSREFS
Sequence in context: A109295 A211188 A057899 * A119989 A137605 A375570
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved