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A144445 Triangle, read by rows, T(n,k) = (7*n-7*k+1)*T(n-1, k-2) + (7*k-6)*T(n-1, k) + 7*T(n-2, k-1) with T(n, 1) = T(n, n) = 1.

%I A144445 #11 Mar 05 2022 01:38:29
%S A144445 1,1,1,1,23,1,1,206,206,1,1,1677,6341,1677,1,1,13452,133451,133451,
%T A144445 13452,1,1,107659,2403612,5916231,2403612,107659,1,1,861322,40024068,
%U A144445 200795987,200795987,40024068,861322,1,1,6890633,638151479,5875203446,11687580863,5875203446,638151479,6890633,1
%N A144445 Triangle, read by rows, T(n,k) = (7*n-7*k+1)*T(n-1, k-2) + (7*k-6)*T(n-1, k) + 7*T(n-2, k-1) with T(n, 1) = T(n, n) = 1.
%H A144445 G. C. Greubel, <a href="/A144445/b144445.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A144445 T(n,k) = (7*n-7*k+1)*T(n-1, k-2) + (7*k-6)*T(n-1, k) + 7*T(n-2, k-1) with T(n, 1) = T(n, n) = 1.
%F A144445 Sum_{k=1..n} T(n, k) = s(n), where s(n) = (7*n-12)*s(n-1) + 7*s(n-2), s(1) = 1, s(2) = 2.
%F A144445 From _G. C. Greubel_, Mar 04 2022: (Start)
%F A144445 T(n, n-k) = T(n, k).
%F A144445 T(n, 2) = (1/7)*(23*8^(n-2) - (7*n+2)).
%F A144445 T(n, 3) = (1/98)*(49*n^2 - 21*n - 59 - 46*(56*n-33)*8^(n-3) + 5989*15^(n-3)). (End)
%e A144445 Triangle begins as:
%e A144445   1;
%e A144445   1,      1;
%e A144445   1,     23,        1;
%e A144445   1,    206,      206,         1;
%e A144445   1,   1677,     6341,      1677,         1;
%e A144445   1,  13452,   133451,    133451,     13452,        1;
%e A144445   1, 107659,  2403612,   5916231,   2403612,   107659,      1;
%e A144445   1, 861322, 40024068, 200795987, 200795987, 40024068, 861322, 1;
%t A144445 T[n_, k_, m_, j_]:= T[n,k,m,j]= If[k==1 || k==n, 1, (m*(n-k)+1)*T[n-1,k-1,m,j] + (m*(k-1)+1)*T[n-1,k,m,j] + j*T[n-2,k-1,m,j] ];
%t A144445 Table[T[n,k,7,7], {n,15}, {k,n}]//Flatten (* modified by _G. C. Greubel_, Mar 04 2022 *)
%o A144445 (Sage)
%o A144445 def T(n,k,m,j):
%o A144445     if (k==1 or k==n): return 1
%o A144445     else: return (m*(n-k)+1)*T(n-1,k-1,m,j) + (m*(k-1)+1)*T(n-1,k,m,j) + j*T(n-2,k-1,m,j)
%o A144445 def A144445(n,k): return T(n,k,7,7)
%o A144445 flatten([[A144445(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Mar 04 2022
%Y A144445 Cf. A144431, A144432, A144435, A144436, A144438, A144439, A144440, A144441, A144442, A144443, A144444.
%K A144445 nonn,tabl
%O A144445 1,5
%A A144445 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 05 2008