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A210866 Triangle of coefficients of polynomials u(n,x) jointly generated with A210867; see the Formula section. 4
1, 1, 1, 1, 3, 1, 1, 6, 6, 2, 1, 10, 21, 14, 3, 1, 15, 55, 65, 31, 5, 1, 21, 120, 235, 187, 65, 8, 1, 28, 231, 700, 867, 503, 134, 13, 1, 36, 406, 1792, 3332, 2914, 1279, 268, 21, 1, 45, 666, 4074, 10955, 13882, 9084, 3122, 527, 34, 1, 55, 1035, 8430, 31563 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row n starts with 1, followed by the n-th triangular number, and ends with the n-th Fibonacci number.

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

LINKS

Table of n, a(n) for n=1..60.

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)-x,

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

EXAMPLE

First five rows:

1

1...1

1...3....1

1...6....6....2

1...10...21...14...3

First three polynomials u(n,x): 1, 1 + x, 1 + 3x + x^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] - 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[%]   (* A210866 *)

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

TableForm[cv]

Flatten[%]   (* A210867 *)

CROSSREFS

Cf. A210867, A208510.

Sequence in context: A172427 A143362 A182823 * A245474 A133713 A008278

Adjacent sequences:  A210863 A210864 A210865 * A210867 A210868 A210869

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 29 2012

STATUS

approved

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Last modified October 17 11:59 EDT 2019. Contains 328110 sequences. (Running on oeis4.)