A208932 Triangle of coefficients of polynomials v(n,x) jointly generated with A208932; see the Formula section.

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.

Links

Table of n, a(n) for n=1..52.

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

Cf. A208930, A208510.

Sequence in context: A249741 A246275 A209757 * A189951 A209776 A019594

Adjacent sequences: A208929 A208930 A208931 * A208933 A208934 A208935

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved