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A207615 Triangle of coefficients of polynomials v(n,x) jointly generated with A207614; the see Formula section. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..60.

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.

EXAMPLE

First five rows:

   1

   3  1

   6  4  1

  12 11  5  1

  24 28 17  6  1

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 *)

CROSSREFS

Cf. A207614, A208510, A003945, A011782.

Sequence in context: A185944 A131415 A210230 * A209165 A121437 A078585

Adjacent sequences:  A207612 A207613 A207614 * A207616 A207617 A207618

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)