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A210861 Triangle of coefficients of polynomials v(n,x) jointly generated with A210860; see the Formula section. 3
1, 2, 2, 6, 7, 3, 16, 30, 20, 5, 50, 116, 108, 47, 8, 156, 460, 552, 338, 105, 13, 532, 1842, 2692, 2119, 941, 221, 21, 1856, 7532, 13072, 12574, 7216, 2452, 451, 34, 6876, 31600, 63240, 71860, 50525, 22371, 6035, 895, 55, 26200, 135576, 308568 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n ends with F(n+1), where F=A000045 (Fibonacci numbers).

Column 1:  A013989

Alternating row sums:  1,0,2,1,3,2,4,3,5,4,...

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..48.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2....2

6....7.....3

16...30....20....5

50...116...108...47...8

First three polynomials v(n,x): 1, 2 + 2x, 6 + 7x + 3x^2

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 14;

u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];

v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x];

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]   (* A210860 *)

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

TableForm[cv]

Flatten[%]   (* A210861 *)

CROSSREFS

Cf. A210860, A208510.

Sequence in context: A305295 A174789 A210865 * A062073 A021445 A011145

Adjacent sequences:  A210858 A210859 A210860 * A210862 A210863 A210864

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 28 2012

STATUS

approved

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)