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A209581
Triangle of coefficients of polynomials u(n,x) jointly generated with A209582; see the Formula section.
3
1, 1, 1, 2, 4, 1, 2, 8, 11, 1, 3, 12, 25, 26, 1, 3, 19, 51, 71, 57, 1, 4, 24, 88, 180, 190, 120, 1, 4, 34, 136, 348, 566, 486, 247, 1, 5, 40, 206, 628, 1238, 1648, 1199, 502, 1, 5, 53, 282, 1034, 2526, 4070, 4545, 2873, 1013, 1, 6, 60, 395, 1600, 4556, 9208
OFFSET
1,4
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+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
1...1
2...4....1
2...8....11...1
3...12...25...26...1
First three polynomials v(n,x): 1, 1 + x, 2 + 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];
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A209581 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209582 *)
CROSSREFS
Sequence in context: A333651 A131398 A249307 * A342053 A050980 A053451
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 11 2012
STATUS
approved