OFFSET
1,2
COMMENTS
Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
FORMULA
u(n,x)=u(n-1,x)+x*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....5
4...12...18...11
5...18...42...49...21
First five polynomials v(n,x):
1
2 + 3x
3 + 7x + 5x^2
4 + 12x + 18x^2 + 11x^3
5 + 18x + 42x^2 + 49x^3 + 21x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 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[%] (* A208524 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208525 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (*A060816*)
Table[v[n, x] /. x -> 1, {n, 1, z}] (*|A084244|*)
Table[u[n, x] /. x -> -1, {n, 1, z}] (*alt. row sums*)
Table[v[n, x] /. x -> -1, {n, 1, z}] (*alt. row sums*)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 29 2012
STATUS
approved