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A167884 Triangle read by rows: T(n,k) 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.

%I A167884 #14 Mar 18 2022 02:50:53
%S A167884 1,1,1,1,18,1,1,179,179,1,1,1636,6086,1636,1,1,14757,144362,144362,
%T A167884 14757,1,1,132854,2941135,7218100,2941135,132854,1,1,1195735,55446309,
%U A167884 277509955,277509955,55446309,1195735,1,1,10761672,1001178268,9211047544,18315657030,9211047544,1001178268,10761672,1
%N A167884 Triangle read by rows: T(n,k) 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.
%H A167884 G. C. Greubel, <a href="/A167884/b167884.txt">Rows n = 1..50 of the triangle, flattened</a>
%H A167884 G. Strasser, <a href="http://dx.doi.org/10.1017/S0305004110000538">Generalisation of the Euler adic</a>, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_8(n,k)
%F A167884 T(n, k) = (m*n-m*k+1)*T(n-1,k-1) + (m*k-m+1)*T(n-1,k), with T(n, 1) = T(n, n) = 1, and m = 8.
%F A167884 Sum_{k=1..n} T(n, k) = A084948(n-1).
%e A167884 Triangle begins as:
%e A167884   1;
%e A167884   1,       1;
%e A167884   1,      18,        1;
%e A167884   1,     179,      179,         1;
%e A167884   1,    1636,     6086,      1636,         1;
%e A167884   1,   14757,   144362,    144362,     14757,        1;
%e A167884   1,  132854,  2941135,   7218100,   2941135,   132854,       1;
%e A167884   1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 1;
%t A167884 T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k-m+1)*T[n-1, k, m]];
%t A167884 A167884[n_, k_]:= T[n,k,8];
%t A167884 Table[A167884[n, k], {n,12}, {k,n}]//Flatten (* modified by _G. C. Greubel_, Mar 18 2022 *)
%o A167884 (Sage)
%o A167884 @CachedFunction
%o A167884 def T(n,k,m):
%o A167884     if (k==1 or k==n): return 1
%o A167884     else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
%o A167884 def A167884(n,k): return T(n,k,8)
%o A167884 flatten([[ A167884(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Mar 18 2022
%Y A167884 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, ...
%Y A167884 Cf. A084948 (row sums).
%K A167884 nonn,tabl,easy
%O A167884 1,5
%A A167884 _Roger L. Bagula_, Nov 14 2009
%E A167884 Edited by _N. J. A. Sloane_, May 08 2013