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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A167884 Triangle read by rows: 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), where m = 8. 5
1, 1, 1, 1, 18, 1, 1, 179, 179, 1, 1, 1636, 6086, 1636, 1, 1, 14757, 144362, 144362, 14757, 1, 1, 132854, 2941135, 7218100, 2941135, 132854, 1, 1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 1, 1, 10761672, 1001178268 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are A084948.

The importance of this recursion is that it gives an integer inverse z transform polynomial set:

p[x_, n_] = x*Sum[a[[n, k]]*x^(k - 1), {k, 1, n}]/(x - 1)^n;

b = Table[p[x, n], {n, 0, 10}];

Table[CoefficientList[ExpandAll[InverseZTransform[b[[k]], x, n] /. UnitStep[ -1 + n] -> 1], n], {k, 1, Length[b]}]

LINKS

Table of n, a(n) for n=1..39.

G. Strasser, Generalisation of the Euler adic, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_8(n,k)

EXAMPLE

{1},

{1, 1},

{1, 18, 1},

{1, 179, 179, 1},

{1, 1636, 6086, 1636, 1},

{1, 14757, 144362, 144362, 14757, 1},

{1, 132854, 2941135, 7218100, 2941135, 132854, 1},

{1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 1},

{1, 10761672, 1001178268, 9211047544, 18315657030, 9211047544, 1001178268, 10761672, 1},

{1, 96855113, 17633445860, 279333923732, 982069631294, 982069631294, 279333923732, 17633445860, 96855113, 1}

MATHEMATICA

Clear[A, p, n, k]

m = 8

A[n_, 1] := 1

A[n_, n_] := 1

A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]

a = Table[A[n, k], {n, 10}, {k, n}]

Flatten[a]

CROSSREFS

For m = ...,-2,-1,0,1,2,3,4,5,6,7,8, ... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, A142459, A142460, A142461, A142462, A167884, ...

Sequence in context: A202677 A179838 A174678 * A022181 A015144 A040332

Adjacent sequences:  A167881 A167882 A167883 * A167885 A167886 A167887

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Nov 14 2009

EXTENSIONS

Edited by N. J. A. Sloane, May 08 2013

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 14:45 EST 2016. Contains 278745 sequences.