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A209582
Triangle of coefficients of polynomials v(n,x) jointly generated with A209581; see the Formula section.
3
1, 2, 3, 2, 6, 7, 3, 10, 17, 15, 3, 16, 39, 46, 31, 4, 21, 69, 129, 119, 63, 4, 30, 112, 260, 386, 296, 127, 5, 36, 172, 492, 890, 1082, 713, 255, 5, 48, 242, 828, 1898, 2832, 2897, 1674, 511, 6, 55, 342, 1318, 3522, 6682, 8511, 7495, 3851, 1023, 6, 70
OFFSET
1,2
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
2...3
2...6....7
3...10...17...15
3...16...39...46...31
First three polynomials v(n,x): 1, 2 + 3x , 2 + 6x + 7x^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: A306156 A276125 A208611 * A158279 A153984 A025502
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 11 2012
STATUS
approved