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A208930
Triangle of coefficients of polynomials v(n,x) jointly generated with A208930; see the Formula section.
4
1, 2, 3, 2, 7, 8, 2, 11, 26, 22, 2, 15, 52, 88, 60, 2, 19, 86, 214, 288, 164, 2, 23, 128, 416, 820, 916, 448, 2, 27, 178, 710, 1824, 2984, 2856, 1224, 2, 31, 236, 1112, 3500, 7464, 10464, 8768, 3344, 2, 35, 302, 1638, 6080, 15884, 29040, 35664, 26592
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...3
2...7....8
2...11...26...22
2...15...52...88...60
First five polynomials v(n,x):
1
2 + 3x
2 + 7x + 8x^2
2 + 11x + 26x^2 + 22x^3
2 + 15x + 52x^2 + 88x^3 + 60x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A208909 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208930 *)
CROSSREFS
Sequence in context: A122697 A129022 A210564 * A122076 A209774 A271322
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 04 2012
STATUS
approved