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

 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 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)