login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208330 Triangle of coefficients of polynomials u(n,x) jointly generated with A208331; see the Formula section. 3
1, 1, 1, 1, 2, 3, 1, 3, 9, 5, 1, 4, 18, 20, 11, 1, 5, 30, 50, 55, 21, 1, 6, 45, 100, 165, 126, 43, 1, 7, 63, 175, 385, 441, 301, 85, 1, 8, 84, 280, 770, 1176, 1204, 680, 171, 1, 9, 108, 420, 1386, 2646, 3612, 3060, 1539, 341, 1, 10, 135, 600, 2310, 5292, 9030 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Subtriangle of the triangle given by (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 18 2012

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

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

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

T(n,k) = A001045(k+1)*binomial(n-1,k). - Philippe Deléham, Mar 18 2012

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1) + 2*T(n-2,k-2), T(1,0) = T(2,0) = T(2,1) = 1, T(n,k) = 0 if k<0 or if k>=n. - Philippe Deléham, Mar 18 2012

EXAMPLE

First five rows:

1

1...1

1...2...3

1...3...9....5

1...4...18...20...11

First five polynomials u(n,x):

1, 1 + x, 1 + 2x + 3x^2, 1 + 3x + 9x^2 + 5x^3, 1 + 4x + 18x^2 + 20x^3 + 11x^4.

(1, 0, 0, 1, 0, 0, ...) DELTA (0, 1, 2, -2, 0, 0, ...) begins :

1

1, 0

1, 1, 0

1, 2, 3, 0

1, 3, 9, 5, 0

1, 4, 18, 20, 11, 0

1, 5, 30, 50, 55, 21, 0. - Philippe Deléham, Mar 18 2012

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 13;

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

v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%]  (* A208330 *)

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

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

TableForm[cv]

Flatten[%]  (* A208331 *)

CROSSREFS

Cf. A208331, A208510.

Sequence in context: A244490 A133935 A139633 * A152440 A134319 A135091

Adjacent sequences:  A208327 A208328 A208329 * A208331 A208332 A208333

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 26 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 12:47 EDT 2019. Contains 328318 sequences. (Running on oeis4.)