login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193894 Mirror of the triangle A193893. 2
1, 4, 2, 44, 28, 12, 210, 150, 90, 36, 680, 520, 360, 208, 80, 1750, 1400, 1050, 710, 400, 150, 3864, 3192, 2520, 1860, 1236, 684, 252, 7644, 6468, 5292, 4130, 3010, 1974, 1078, 392, 13920, 12000, 10080, 8176, 6320, 4560, 2960, 1600, 576, 23760 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A193894 is obtained by reversing the rows of the triangle A193893.

LINKS

Table of n, a(n) for n=0..45.

FORMULA

Write w(n,k) for the triangle at A193893.  The triangle at A193894 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

4.....2

44....28....12

210...150...90....36

680...520...360...208..80

1750..1400..1050..710..400..105

MATHEMATICA

z = 9;

p[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - k), {k, 0, n}]

q[n_, x_] := p[n, x];

t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

g[n_] := CoefficientList[w[n, x], {x}]

TableForm[Table[Reverse[g[n]], {n, -1, z}]]

Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193893 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193894 *)

CROSSREFS

Cf. A193893.

Sequence in context: A280780 A264755 A120968 * A107667 A163176 A277306

Adjacent sequences:  A193891 A193892 A193893 * A193895 A193896 A193897

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

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 September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)