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A209749
Triangle of coefficients of polynomials u(n,x) jointly generated with A209750; see the Formula section.
3
1, 1, 2, 2, 4, 3, 2, 8, 9, 4, 3, 11, 21, 17, 5, 3, 17, 37, 47, 29, 6, 4, 21, 63, 101, 95, 46, 7, 4, 29, 93, 193, 241, 178, 69, 8, 5, 34, 138, 329, 519, 522, 314, 99, 9, 5, 44, 186, 533, 999, 1264, 1050, 527, 137, 10, 6, 50, 255, 805, 1776, 2710, 2845, 1991, 848
OFFSET
1,3
COMMENTS
Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
2...4....3
2...8....9....4
3...11...21...17...5
First three polynomials u(n,x): 1, 1 + 2x, 2 + 4x + 3x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + 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[%] (* A209749 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209750 *)
CROSSREFS
Sequence in context: A355476 A328932 A341148 * A248345 A094953 A332862
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 14 2012
STATUS
approved