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A209580
Triangle of coefficients of polynomials v(n,x) jointly generated with A209579; see the Formula section.
3
1, 2, 2, 2, 4, 3, 3, 7, 8, 4, 3, 11, 19, 15, 5, 4, 15, 34, 43, 26, 6, 4, 21, 57, 91, 87, 42, 7, 5, 26, 87, 176, 217, 163, 64, 8, 5, 34, 126, 301, 473, 472, 288, 93, 9, 6, 40, 176, 489, 908, 1150, 954, 485, 130, 10, 6, 50, 235, 745, 1626, 2460, 2587, 1817, 784
OFFSET
1,2
COMMENTS
Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
2...4....3
3...7....8....4
3...11...19...15...1
First three polynomials v(n,x): 1, 2 + 2x , 2 + 4x + 3x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := (x + 1)*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[%] (* A209579 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209580 *)
CROSSREFS
Sequence in context: A085454 A083403 A114091 * A166008 A194291 A194323
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 11 2012
STATUS
approved