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A209145
Triangle of coefficients of polynomials u(n,x) jointly generated with A122075; see the Formula section.
2
1, 2, 1, 4, 4, 1, 7, 10, 5, 1, 12, 22, 16, 6, 1, 20, 45, 43, 23, 7, 1, 33, 88, 104, 72, 31, 8, 1, 54, 167, 235, 199, 110, 40, 9, 1, 88, 310, 506, 506, 340, 158, 50, 10, 1, 143, 566, 1051, 1211, 956, 538, 217, 61, 11, 1, 232, 1020, 2123, 2768, 2507, 1652, 805
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=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....1
4....4....1
7....10...5....1
12...22...16...6...1
MATHEMATICA
First three polynomials v(n, x): 1, 2 + 3x, 4 + 4x + 4x^2.
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 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[%] (* A209145 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A122075 *)
CROSSREFS
Sequence in context: A220836 A008572 A209150 * A333650 A214984 A118976
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 06 2012
STATUS
approved