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A207614
Triangle of coefficients of polynomials u(n,x) jointly generated with A207615; see the Formula section.
3
1, 2, 5, 1, 11, 5, 1, 23, 16, 6, 1, 47, 44, 23, 7, 1, 95, 112, 74, 31, 8, 1, 191, 272, 216, 113, 40, 9, 1, 383, 640, 592, 368, 162, 50, 10, 1, 767, 1472, 1552, 1112, 579, 222, 61, 11, 1, 1535, 3328, 3936, 3184, 1902, 861, 294, 73, 12, 1, 3071, 7424, 9728
OFFSET
1,2
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=u(n-1,x)+(x+1)v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2
5....1
11...5....1
23...16...6...1
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A207614 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207615 *)
CROSSREFS
Cf. A207615.
Sequence in context: A323411 A089618 A207629 * A156067 A352577 A263487
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved