login
A208932
Triangle of coefficients of polynomials v(n,x) jointly generated with A208932; see the Formula section.
3
1, 3, 2, 5, 8, 4, 7, 22, 24, 8, 9, 48, 84, 60, 16, 11, 90, 228, 264, 148, 32, 13, 152, 528, 876, 772, 348, 64, 15, 238, 1092, 2424, 2992, 2112, 804, 128, 17, 352, 2072, 5896, 9568, 9392, 5548, 1820, 256, 19, 498, 3672, 13008, 26648, 34080, 27780
OFFSET
1,2
COMMENTS
Alternating row sums: 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)+2x*v(n-1,x),
v(n,x)=(x+1)*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
3...2
5...8....4
7...22...24...8
9...48...84...60...16
First five polynomials v(n,x):
1
3 + 2x
5 + 8x + 4x^2
7 + 22x + 24x^2 + 8x^3
9 + 48x + 84x^2 + 60x^3 + 16x^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_] := (x + 1)*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[%] (* A208931 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208932 *)
CROSSREFS
Sequence in context: A249741 A246275 A209757 * A189951 A209776 A019594
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 04 2012
STATUS
approved