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A210862 Triangle of coefficients of polynomials u(n,x) jointly generated with A210863; see the Formula section. 3
1, 2, 1, 3, 2, 2, 4, 6, 7, 3, 5, 15, 20, 16, 5, 6, 31, 57, 63, 37, 8, 7, 56, 153, 215, 184, 81, 13, 8, 92, 370, 684, 771, 513, 171, 21, 9, 141, 805, 2028, 2898, 2603, 1354, 351, 34, 10, 205, 1598, 5515, 10084, 11582, 8319, 3415, 703, 55, 11, 286, 2940 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).

Column 2:  A056520

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

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...2....2

4...6....7....3

5...15...20...16...5

First three polynomials u(n,x): 1, 2 + x, 4 + 5x + 2x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + n - 1)*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[%]   (* A210862 *)

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

TableForm[cv]

Flatten[%]   (* A210863 *)

CROSSREFS

Cf. A210863, A208510.

Sequence in context: A120933 A209756 A210795 * A298675 A144154 A054710

Adjacent sequences:  A210859 A210860 A210861 * A210863 A210864 A210865

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 28 2012

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)