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A207621 Triangle of coefficients of polynomials v(n,x) jointly generated with A207620; the see Formula section. 3
1, 2, 2, 3, 6, 2, 4, 13, 10, 2, 5, 24, 31, 14, 2, 6, 40, 76, 57, 18, 2, 7, 62, 161, 176, 91, 22, 2, 8, 91, 308, 456, 340, 133, 26, 2, 9, 128, 546, 1044, 1045, 584, 183, 30, 2, 10, 174, 912, 2178, 2794, 2080, 924, 241, 34, 2, 11, 230, 1452, 4224, 6721, 6370 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

v(n,x)=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

2...2

3..,6...2

4...13...10...2

5...24...31...14...2

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] + (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[%]    (* A207620 *)

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

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

TableForm[cv]

Flatten[%]    (* A207621 *)

CROSSREFS

Cf. A207620.

Sequence in context: A083506 A248164 A210222 * A209157 A284785 A076333

Adjacent sequences:  A207618 A207619 A207620 * A207622 A207623 A207624

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 15 07:42 EDT 2019. Contains 328026 sequences. (Running on oeis4.)