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%I #11 Mar 13 2023 06:07:32
%S 1,1,3,1,5,11,1,13,31,55,1,49,121,217,337,1,241,601,1081,1681,2401,1,
%T 1441,3601,6481,10081,14401,19441,1,10081,25201,45361,70561,100801,
%U 136081,176401,1,80641,201601,362881,564481,806401,1088641,1411201,1774081
%N Triangle, read by rows, T(n, k) = T(n, k-1) + (k+1)*n!, T(n, 0) = 1.
%H G. C. Greubel, <a href="/A105064/b105064.txt">Rows n = 0..50 of the triangle, flattened</a>
%F From _G. C. Greubel_, Mar 12 2023: (Start)
%F T(n, k) = T(n, k-1) + (k+1)*n!, T(n, 0) = 1.
%F T(n, n-1) = (1/2)*((n^2 + n - 2)*n! + 2).
%F T(n, n) = (1/2)*(n*(n+3)*n! + 2). (End)
%e Triangle begins:
%e 1;
%e 1, 3;
%e 1, 5, 11;
%e 1, 13, 31, 55;
%e 1, 49, 121, 217, 337;
%e 1, 241, 601, 1081, 1681, 2401;
%e ...
%t T[n_, k_]:= T[n, k]= If[k==0, 1, T[n, k-1] +(k+1)*n!];
%t Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten
%o (Magma)
%o function T(n,k) // T = A105064
%o if k eq 0 then return 1;
%o else return T(n,k-1) + (k+1)*Factorial(n);
%o end if; return T;
%o end function;
%o [T(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 12 2023
%o (SageMath)
%o def T(n,k): # T = A105064
%o if (k==0): return 1
%o else: return T(n,k-1) + (k+1)*factorial(n)
%o flatten([[T(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Mar 12 2023
%K nonn,tabl
%O 0,3
%A _Roger L. Bagula_, Apr 05 2005
%E Edited by _G. C. Greubel_, Mar 12 2023
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