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A209162
Triangle of coefficients of polynomials u(n,x) jointly generated with A209163; see the Formula section.
3
1, 2, 1, 4, 6, 3, 7, 18, 17, 5, 11, 42, 63, 42, 11, 16, 85, 183, 195, 103, 21, 22, 156, 452, 678, 558, 240, 43, 29, 266, 994, 1966, 2252, 1510, 553, 85, 37, 428, 2002, 5012, 7494, 6946, 3929, 1246, 171, 46, 657, 3762, 11586, 21702, 26060, 20265, 9909
OFFSET
1,2
COMMENTS
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+(x+1)*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....1
4....6....3
7....18...17...5
11...42...63...42...11
First three polynomials v(n,x): 1, 2 + x, 4 + 6x + 3x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*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[%] (* A209162 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209163 *)
CROSSREFS
Sequence in context: A180405 A171007 A209168 * A127366 A064786 A367286
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 07 2012
STATUS
approved