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A207610 Triangle of coefficients of polynomials u(n,x) jointly generated with A207611; see the Formula section. 3
1, 2, 4, 1, 7, 3, 1, 12, 7, 3, 1, 20, 15, 8, 3, 1, 33, 30, 19, 9, 3, 1, 54, 58, 42, 23, 10, 3, 1, 88, 109, 89, 55, 27, 11, 3, 1, 143, 201, 182, 125, 69, 31, 12, 3, 1, 232, 365, 363, 273, 166, 84, 35, 13, 3, 1, 376, 655, 709, 579, 383, 212, 100, 39, 14, 3, 1, 609 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1:  A000071

Column 2:  A023610

LINKS

Table of n, a(n) for n=1..68.

FORMULA

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

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

EXAMPLE

First five rows:

1

2

4...1

7...3...1

12...7...3...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*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[%]    (* A207610 *)

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

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

TableForm[cv]

Flatten[%]    (* A207611 *)

PROG

(Python)

from sympy import Poly

def u(n, x): return 1 if n==1 else u(n - 1, x) + v(n - 1, x)

def v(n, x): return 1 if n==1 else u(n - 1, x) + x*v(n - 1, x) + 1

def a(n): return Poly(u(n, x), x).all_coeffs()[::-1]

for n in xrange(1, 13): print a(n) # Indranil Ghosh, May 28 2017

CROSSREFS

Cf. A207611.

Sequence in context: A302541 A119303 A256107 * A207616 A105552 A112852

Adjacent sequences:  A207607 A207608 A207609 * A207611 A207612 A207613

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 19 2012

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)