A167884 - OEIS

%I #14 Mar 18 2022 02:50:53

%S 1,1,1,1,18,1,1,179,179,1,1,1636,6086,1636,1,1,14757,144362,144362,

%T 14757,1,1,132854,2941135,7218100,2941135,132854,1,1,1195735,55446309,

%U 277509955,277509955,55446309,1195735,1,1,10761672,1001178268,9211047544,18315657030,9211047544,1001178268,10761672,1

%N 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 G. C. Greubel, <a href="/A167884/b167884.txt">Rows n = 1..50 of the triangle, flattened</a>

%H 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 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 Sum_{k=1..n} T(n, k) = A084948(n-1).

%e Triangle begins as:

%e   1;

%e   1,       1;

%e   1,      18,        1;

%e   1,     179,      179,         1;

%e   1,    1636,     6086,      1636,         1;

%e   1,   14757,   144362,    144362,     14757,        1;

%e   1,  132854,  2941135,   7218100,   2941135,   132854,       1;

%e   1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 1;

%t 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[n_, k_]:= T[n,k,8];

%t Table[A167884[n, k], {n,12}, {k,n}]//Flatten (* modified by _G. C. Greubel_, Mar 18 2022 *)

%o (Sage)

%o @CachedFunction

%o def T(n,k,m):

%o     if (k==1 or k==n): return 1

%o     else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)

%o def A167884(n,k): return T(n,k,8)

%o flatten([[ A167884(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Mar 18 2022

%Y 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 Cf. A084948 (row sums).

%K nonn,tabl,easy

%O 1,5

%A _Roger L. Bagula_, Nov 14 2009

%E Edited by _N. J. A. Sloane_, May 08 2013