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A210756 Triangle of coefficients of polynomials v(n,x) jointly generated with A210755; see the Formula section. 3
1, 3, 2, 6, 10, 5, 10, 30, 33, 12, 15, 70, 127, 100, 29, 21, 140, 371, 472, 291, 70, 28, 252, 910, 1656, 1624, 822, 169, 36, 420, 1974, 4800, 6640, 5294, 2273, 408, 45, 660, 3906, 12144, 22166, 24702, 16589, 6184, 985, 55, 990, 7194, 27720, 63954 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1: triangular numbers, A000217

Coefficient of v(n,x):  A000129(n)

Row sums:  A002450

Alternating row sums: 1,1,1,1,1,1,1,1,1,...

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

LINKS

Table of n, a(n) for n=1..50.

FORMULA

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

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

3....2

6....10...5

10...30...33....12

15...70...127...100...29

First three polynomials v(n,x): 1, 3 + 2x, 6 + 10x + 5x^2

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;

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

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[%]    (* A210755 *)

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

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

TableForm[cv]

Flatten[%]    (* A210756 *)

Table[u[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)

Table[v[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)

CROSSREFS

Cf. A210755, A208510.

Sequence in context: A171632 A245609 A072765 * A210748 A109876 A108284

Adjacent sequences:  A210753 A210754 A210755 * A210757 A210758 A210759

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 25 2012

STATUS

approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)