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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.
7

%I #12 Mar 17 2022 23:56:29

%S 1,1,1,1,16,1,1,143,143,1,1,1166,4290,1166,1,1,9357,90002,90002,9357,

%T 1,1,74892,1621383,3960088,1621383,74892,1,1,599179,27016857,

%U 134142043,134142043,27016857,599179,1,1,4793482,431017552,3923731798,7780238494,3923731798,431017552,4793482,1

%N 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 G. C. Greubel, <a href="/A142462/b142462.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_7(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 = 7.

%F Sum_{k=1..n} T(n, k) = A084947(n-1).

%e Triangle begins as:

%e 1;

%e 1, 1;

%e 1, 16, 1;

%e 1, 143, 143, 1;

%e 1, 1166, 4290, 1166, 1;

%e 1, 9357, 90002, 90002, 9357, 1;

%e 1, 74892, 1621383, 3960088, 1621383, 74892, 1;

%e 1, 599179, 27016857, 134142043, 134142043, 27016857, 599179, 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 A142462[n_, k_]:= T[n,k,7];

%t Table[A142462[n, k], {n,12}, {k,n}]//Flatten (* modified by _G. C. Greubel_, Mar 17 2022 *)

%o (Magma)

%o function T(n,k,m)

%o if k eq 1 or k eq n then 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 end if; return T;

%o end function;

%o A142462:= func< n,k | T(n,k,7) >;

%o [A142462(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Mar 17 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 A142462(n,k): return T(n,k,7)

%o flatten([[ A142462(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Mar 17 2022

%Y 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 Cf. A084947 (row sums).

%K nonn,tabl,easy

%O 1,5

%A _Roger L. Bagula_, Sep 19 2008

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