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A207627
Triangle of coefficients of polynomials u(n,x) jointly generated with A207628; see the Formula section.
3
1, 2, 3, 4, 4, 10, 8, 5, 18, 28, 16, 6, 28, 64, 72, 32, 7, 40, 120, 200, 176, 64, 8, 54, 200, 440, 576, 416, 128, 9, 70, 308, 840, 1456, 1568, 960, 256, 10, 88, 448, 1456, 3136, 4480, 4096, 2176, 512, 11, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864
OFFSET
1,2
COMMENTS
Column n is divisible by 2^(n-1); row n ends with 2^(n-1).
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x),
v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
The row sums =: 2, 7, 22, 67, ... are given by (5*3^n -1)/2 for n = 0, 1, 2, 3, ... . - Philippe Deléham, Feb 25 2012
EXAMPLE
First five rows:
1
2
3...4
4...10...8
5...18...28...16
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_] := 2 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[%] (* A207625 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207626 *)
CROSSREFS
Cf. A207628.
Sequence in context: A118263 A217478 A279788 * A102539 A240220 A250229
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Feb 21 2012
STATUS
approved