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A210858 Triangle of coefficients of polynomials u(n,x) jointly generated with A210859; see the Formula section. 3
1, 1, 1, 1, 3, 2, 1, 6, 8, 3, 1, 10, 24, 20, 5, 1, 15, 59, 82, 45, 8, 1, 21, 125, 271, 251, 98, 13, 1, 28, 237, 765, 1073, 701, 204, 21, 1, 36, 413, 1898, 3860, 3802, 1842, 414, 34, 1, 45, 674, 4235, 12115, 17011, 12325, 4589, 820, 55, 1, 55, 1044, 8662 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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

Alternating row sums:  1,0,0,0,0,0,0,0,...

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

LINKS

Table of n, a(n) for n=1..59.

FORMULA

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

1...1

1...3....2

1...6....8....3

1...10...24...20...5

First three polynomials u(n,x): 1, 1 + x, 1 + 3x + 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];

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[%]   (* A210858 *)

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

TableForm[cv]

Flatten[%]   (* A210859 *)

CROSSREFS

Cf. A210806, A208510.

Sequence in context: A132276 A257558 A202390 * A114586 A052174 A227790

Adjacent sequences:  A210855 A210856 A210857 * A210859 A210860 A210861

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 28 2012

STATUS

approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)