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A210194
Triangle of coefficients of polynomials v(n,x) jointly generated with A210193; see the Formula section.
3
1, 2, 3, 3, 11, 3, 4, 26, 20, 3, 5, 50, 74, 29, 3, 6, 85, 204, 149, 38, 3, 7, 133, 469, 547, 251, 47, 3, 8, 196, 952, 1618, 1160, 380, 56, 3, 9, 276, 1764, 4110, 4234, 2124, 536, 65, 3, 10, 375, 3048, 9318, 13036, 9262, 3520, 719, 74, 3, 11, 495, 4983
OFFSET
1,2
COMMENTS
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)=2x*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
2...3
3...11...3
4...26...20...3
5...50...74...29...3
First three polynomials v(n,x): 1, 2 + 3x , 3 + 11x + 3x^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_] := 2 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[%] (* A210193 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210194 *)
CROSSREFS
Sequence in context: A117030 A155758 A009097 * A210755 A219224 A265532
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved