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A208920 Triangle of coefficients of polynomials v(n,x) jointly generated with A208919; see the Formula section. 3
1, 2, 3, 3, 7, 7, 4, 12, 26, 19, 5, 18, 62, 85, 47, 6, 25, 120, 235, 264, 123, 7, 33, 205, 515, 879, 803, 311, 8, 42, 322, 980, 2254, 3038, 2358, 803, 9, 52, 476, 1694, 4914, 8708, 10156, 6865, 2047, 10, 63, 672, 2730, 9576, 20958, 32640, 32877, 19588 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=2x*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...3
3...7....7
4...12...26...19
5...18...62...85...47
First five polynomials v(n,x):
1
2 + 3x
3 + 7x + 7x^2
4 + 12x + 26x^2 + 19x^3
5 + 18x + 62x^2 + 85x^3 + 47x^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_] := 2 x*u[n - 1, x] + (x + 1)*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[%] (* A208919 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208920 *)
CROSSREFS
Sequence in context: A143444 A108346 A210558 * A210234 A209768 A209169
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 04 2012
STATUS
approved

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Last modified May 23 18:13 EDT 2024. Contains 372765 sequences. (Running on oeis4.)