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A207633 Triangle of coefficients of polynomials u(n,x) jointly generated with A207634; see the Formula section. 3
1, 2, 4, 3, 7, 9, 6, 12, 22, 21, 12, 20, 48, 62, 48, 24, 33, 98, 157, 163, 108, 48, 54, 192, 367, 463, 410, 240, 96, 88, 365, 810, 1203, 1281, 1000, 528, 192, 143, 679, 1715, 2919, 3634, 3392, 2384, 1152, 384, 232, 1242, 3518, 6742, 9550, 10379, 8696 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2

4....3

7....9....6

12...22...21...12

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 + 1)*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[%]  (* A207633 *)

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

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

TableForm[cv]

Flatten[%]  (* A207634 *)

CROSSREFS

Cf. A207634.

Sequence in context: A246268 A246267 A101267 * A177877 A090568 A223625

Adjacent sequences:  A207630 A207631 A207632 * A207634 A207635 A207636

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 24 2012

STATUS

approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)