A207615 Triangle of coefficients of polynomials v(n,x) jointly generated with A207614; see the Formula section.

1, 3, 1, 6, 4, 1, 12, 11, 5, 1, 24, 28, 17, 6, 1, 48, 68, 51, 24, 7, 1, 96, 160, 142, 82, 32, 8, 1, 192, 368, 376, 255, 122, 41, 9, 1, 384, 832, 960, 744, 417, 172, 51, 10, 1, 768, 1856, 2384, 2072, 1323, 639, 233, 62, 11, 1, 1536, 4096, 5792, 5568, 3974

Offset: 1

Author

Clark Kimberling, Feb 20 2012

Keywords

• nonn
• tabl
• easy

Comments

Riordan array ((1 + z)/(1 - 2*z), z*(1 - z)/(1 - 2*z)). - Peter Bala, Dec 31 2015

Examples

			First five rows:
   1
   3  1
   6  4  1
  12 11  5  1
  24 28 17  6  1
		

Crossrefs

Cf. A207614, A208510, A003945, A011782.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A207614 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207615 *)

Formula

u(n,x) = u(n-1,x) + v(n-1,x),

v(n,x) = u(n-1,x) + (x + 1)*v(n-1,x) + 1,

where u(1,x) = 1, v(1,x) = 1.