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A207619 Triangle of coefficients of polynomials v(n,x) jointly generated with A207618; the see Formula section. 3
1, 1, 3, 1, 4, 6, 1, 5, 11, 12, 1, 6, 17, 28, 24, 1, 7, 24, 51, 68, 48, 1, 8, 32, 82, 142, 160, 96, 1, 9, 41, 122, 255, 376, 368, 192, 1, 10, 51, 172, 417, 744, 960, 832, 384, 1, 11, 62, 233, 639, 1323, 2072, 2384, 1856, 768, 1, 12, 74, 306, 933, 2184, 3974 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..62.

FORMULA

u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=xu(n-1,x)+2x*v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

1...3

1...4...6

1...5...11...12

1...6...17...28...24

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_] := x*u[n - 1, x] + 2 x*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[%]    (* A207618 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A207619 *)

CROSSREFS

Cf. A207618.

Sequence in context: A080851 A209518 A108285 * A209694 A286951 A260355

Adjacent sequences:  A207616 A207617 A207618 * A207620 A207621 A207622

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)