login
A208607
Triangle of coefficients of polynomials v(n,x) jointly generated with A208606; see the Formula section.
3
1, 3, 1, 5, 3, 1, 7, 8, 6, 1, 9, 18, 19, 6, 1, 11, 35, 47, 25, 9, 1, 13, 61, 102, 81, 42, 9, 1, 15, 98, 203, 219, 147, 51, 12, 1, 17, 148, 378, 520, 435, 216, 74, 12, 1, 19, 213, 666, 1122, 1145, 747, 334, 86, 15, 1, 21, 295, 1119, 2250, 2753, 2233, 1245, 450
OFFSET
1,2
COMMENTS
Alternating rows sums: 1,2,3,4,5,6,7,8,...
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3...1
5...3...1
7...8...6...1
9...18...19...6...1
First five polynomials v(n,x):
1
3 + x
5 + 3x + x^2
7 + 8x + 6x^2 + x^3
9 + 18x + 19x^2 + 6x^3 + x^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] + 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[%] (* A208606 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208607 *)
CROSSREFS
Cf. A208606.
Sequence in context: A258207 A133094 A300437 * A159291 A122510 A102662
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 29 2012
STATUS
approved