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A142462 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 = 7.

%I A142462 #12 Mar 17 2022 23:56:29
%S A142462 1,1,1,1,16,1,1,143,143,1,1,1166,4290,1166,1,1,9357,90002,90002,9357,
%T A142462 1,1,74892,1621383,3960088,1621383,74892,1,1,599179,27016857,
%U A142462 134142043,134142043,27016857,599179,1,1,4793482,431017552,3923731798,7780238494,3923731798,431017552,4793482,1
%N A142462 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 = 7.
%H A142462 G. C. Greubel, <a href="/A142462/b142462.txt">Rows n = 1..50 of the triangle, flattened</a>
%H A142462 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_7(n,k).
%F A142462 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 = 7.
%F A142462 Sum_{k=1..n} T(n, k) = A084947(n-1).
%e A142462 Triangle begins as:
%e A142462   1;
%e A142462   1,      1;
%e A142462   1,     16,        1;
%e A142462   1,    143,      143,         1;
%e A142462   1,   1166,     4290,      1166,         1;
%e A142462   1,   9357,    90002,     90002,      9357,        1;
%e A142462   1,  74892,  1621383,   3960088,   1621383,    74892,      1;
%e A142462   1, 599179, 27016857, 134142043, 134142043, 27016857, 599179, 1;
%t A142462 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 A142462 A142462[n_, k_]:= T[n,k,7];
%t A142462 Table[A142462[n, k], {n,12}, {k,n}]//Flatten (* modified by _G. C. Greubel_, Mar 17 2022 *)
%o A142462 (Magma)
%o A142462 function T(n,k,m)
%o A142462   if k eq 1 or k eq n then return 1;
%o A142462   else return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m);
%o A142462   end if; return T;
%o A142462 end function;
%o A142462 A142462:= func< n,k | T(n,k,7) >;
%o A142462 [A142462(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Mar 17 2022
%o A142462 (Sage)
%o A142462 @CachedFunction
%o A142462 def T(n,k,m):
%o A142462     if (k==1 or k==n): return 1
%o A142462     else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
%o A142462 def A142462(n,k): return T(n,k,7)
%o A142462 flatten([[ A142462(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Mar 17 2022
%Y A142462 For m = ...,-2,-1,0,1,2,3,4,5,6,7, ... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, A142459, A142460, A142461, A142462, ...
%Y A142462 Cf. A084947 (row sums).
%K A142462 nonn,tabl,easy
%O A142462 1,5
%A A142462 _Roger L. Bagula_, Sep 19 2008
%E A142462 Edited by _N. J. A. Sloane_, May 08 2013