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A207635
Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section.
3
1, 2, 5, 2, 11, 9, 2, 23, 29, 13, 2, 47, 81, 55, 17, 2, 95, 209, 191, 89, 21, 2, 191, 513, 591, 369, 131, 25, 2, 383, 1217, 1695, 1329, 631, 181, 29, 2, 767, 2817, 4607, 4353, 2591, 993, 239, 33, 2, 1535, 6401, 12031, 13313, 9535, 4577, 1471, 305, 37, 2
OFFSET
1,2
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x),
v(n,x)=(x+1)*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....2
11...9....2
23...29...13...2
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_] := (x + 1)*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[%] (* A207635 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207636 *)
CROSSREFS
Cf. A207636.
Sequence in context: A276609 A292591 A240760 * A205715 A181338 A211175
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Feb 24 2012
STATUS
approved