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A207615
Triangle of coefficients of polynomials v(n,x) jointly generated with A207614; see the Formula section.
4
1, 3, 1, 6, 4, 1, 12, 11, 5, 1, 24, 28, 17, 6, 1, 48, 68, 51, 24, 7, 1, 96, 160, 142, 82, 32, 8, 1, 192, 368, 376, 255, 122, 41, 9, 1, 384, 832, 960, 744, 417, 172, 51, 10, 1, 768, 1856, 2384, 2072, 1323, 639, 233, 62, 11, 1, 1536, 4096, 5792, 5568, 3974
OFFSET
1,2
COMMENTS
Riordan array ((1 + z)/(1 - 2*z), z*(1 - z)/(1 - 2*z)). - Peter Bala, Dec 31 2015
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
3 1
6 4 1
12 11 5 1
24 28 17 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
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved