A208525 Triangle of coefficients of polynomials v(n,x) jointly generated with A208524; see the Formula section.

1, 2, 3, 3, 7, 5, 4, 12, 18, 11, 5, 18, 42, 49, 21, 6, 25, 80, 135, 116, 43, 7, 33, 135, 295, 381, 279, 85, 8, 42, 210, 560, 966, 1050, 638, 171, 9, 52, 308, 966, 2086, 2996, 2724, 1453, 341, 10, 63, 432, 1554, 4032, 7182, 8688, 6921, 3240, 683, 11, 75

Offset

1,2

Comments

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...

Links

Table of n, a(n) for n=1..57.

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

Cf. A208524.

Sequence in context: A088100 A097359 A358182 * A342878 A209574 A079387

Adjacent sequences: A208522 A208523 A208524 * A208526 A208527 A208528

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 29 2012

Status

approved