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!)
A142458 Triangle T(n,k) (1 <= k <= n) read by rows: T(n,k) = 1 if k=1 or k=n, else T(n,k) = (3*n-3*k+1)*T(n-1,k-1) + (3*k-2)*T(n-1,k). 35
1, 1, 1, 1, 8, 1, 1, 39, 39, 1, 1, 166, 546, 166, 1, 1, 677, 5482, 5482, 677, 1, 1, 2724, 47175, 109640, 47175, 2724, 1, 1, 10915, 373809, 1709675, 1709675, 373809, 10915, 1, 1, 43682, 2824048, 23077694, 44451550, 23077694, 2824048, 43682, 1, 1, 174753 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Consider the triangle T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1)+(m*k-m+1)*T(n-1,k).

For m = ...,-2,-1,0,1,2,3,... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, ... - N. J. A. Sloane, May 08 2013

Row sums are 1, 2, 10, 80, 880, 12320, 209440, 4188800, 96342400, 2504902400,.., (see A008544)

LINKS

Table of n, a(n) for n=1..47.

G. Strasser, Generalisation of the Euler adic, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_3(n,k).

EXAMPLE

The rows n>=1 and columns 1<=k<=n look as follows:

1;

1, 1;

1, 8, 1;

1, 39, 39, 1;

1, 166, 546, 166, 1;

1, 677, 5482, 5482, 677, 1;

1, 2724, 47175, 109640, 47175, 2724, 1;

1, 10915, 373809, 1709675, 1709675, 373809, 10915, 1;

1, 43682, 2824048, 23077694, 44451550, 23077694, 2824048, 43682, 1;

1, 174753, 20729340, 284433852, 947113254, 947113254, 284433852, 20729340, 174753, 1;

MAPLE

A142458 := proc(n, k) if n = k then 1; elif k > n or k < 1 then 0 ; else (3*n-3*k+1)*procname(n-1, k-1)+(3*k-2)*procname(n-1, k) ; end if; end proc:

seq(seq(A142458(n, k), k=1..n), n=1..10) ; # R. J. Mathar, Jun 04 2011

MATHEMATICA

A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (3*n - 3*k + 1)A[n - 1, k - 1] + (3*k - 2)A[n - 1, k]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]

CROSSREFS

Cf. A225372, A144431, A007318, A008292, A060187.

Sequence in context: A152972 A166346 A157640 * A174528 A259465 A176227

Adjacent sequences:  A142455 A142456 A142457 * A142459 A142460 A142461

KEYWORD

nonn,easy,tabl

AUTHOR

Roger L. Bagula, Sep 19 2008

EXTENSIONS

Edited by the Associate Editors of the OEIS, Aug 28 2009

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 April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)