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A208610
Triangle of coefficients of polynomials u(n,x) jointly generated with A208611; see the Formula section.
3
1, 1, 1, 1, 3, 3, 1, 5, 9, 7, 1, 7, 17, 25, 17, 1, 9, 27, 55, 69, 41, 1, 11, 39, 99, 171, 187, 99, 1, 13, 53, 159, 341, 515, 501, 239, 1, 15, 69, 237, 599, 1125, 1515, 1329, 577, 1, 17, 87, 335, 967, 2141, 3591, 4373, 3497, 1393, 1, 19, 107, 455, 1469, 3713
OFFSET
1,5
FORMULA
u(n,x)=u(n-1,x)+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
1...3...3
1...5...9...7
1...7...17...25...17
First five polynomials u(n,x):
1
1 + x
1 + 3x + 3x^2
1 + 5x + 9x^2 + 7x^3
1 + 7x + 17x^2 + 25x^3 + 17x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 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[%] (* A208610 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208611 *)
CROSSREFS
Cf. A208611.
Sequence in context: A164984 A248810 A339904 * A193823 A071945 A209583
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 01 2012
STATUS
approved