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A135902 Triangle T, read by rows, where column k of T = column 0 of T^(k+1) for k>0, with column 0 of T = column 0 of T^3 shift right.

%I A135902 #4 Jun 14 2017 00:57:39
%S A135902 1,1,1,3,2,1,15,8,3,1,102,47,15,4,1,860,356,102,24,5,1,8548,3252,860,
%T A135902 186,35,6,1,97094,34448,8548,1736,305,48,7,1,1234324,412546,97094,
%U A135902 18754,3130,465,63,8,1,17302880,5488222,1234324,228658,36630,5212,672,80,9,1
%N A135902 Triangle T, read by rows, where column k of T = column 0 of T^(k+1) for k>0, with column 0 of T = column 0 of T^3 shift right.
%C A135902 This is a variant of permutation triangle P = A094587, A094587(n,k) = n!/k!, which may be defined by: triangular matrix P where column k of P = column 0 of P^(k+1), with column 0 of P = column 0 of P^2 shift right.
%F A135902 Column k of T^(j+1) = column j of T^(k+1) for j>=0, k>=0.
%e A135902 Triangle T begins:
%e A135902 1;
%e A135902 1, 1;
%e A135902 3, 2, 1;
%e A135902 15, 8, 3, 1;
%e A135902 102, 47, 15, 4, 1;
%e A135902 860, 356, 102, 24, 5, 1;
%e A135902 8548, 3252, 860, 186, 35, 6, 1;
%e A135902 97094, 34448, 8548, 1736, 305, 48, 7, 1;
%e A135902 1234324, 412546, 97094, 18754, 3130, 465, 63, 8, 1;
%e A135902 17302880, 5488222, 1234324, 228658, 36630, 5212, 672, 80, 9, 1; ...
%e A135902 where column k of T = column 0 of T^(k+1)
%e A135902 with column 0 of T = column 0 of T^3 shift right.
%e A135902 Matrix square of T, T^2, begins:
%e A135902 1;
%e A135902 2, 1;
%e A135902 8, 4, 1;
%e A135902 47, 22, 6, 1;
%e A135902 356, 156, 42, 8, 1;
%e A135902 3252, 1343, 351, 68, 10, 1;
%e A135902 34448, 13493, 3415, 656, 100, 12, 1; ...
%e A135902 where column 0 of T^2 = column 1 of T.
%e A135902 Matrix cube of T, T^3, begins:
%e A135902 1;
%e A135902 3, 1;
%e A135902 15, 6, 1;
%e A135902 102, 42, 9, 1;
%e A135902 860, 351, 81, 12, 1;
%e A135902 8548, 3415, 807, 132, 15, 1;
%e A135902 97094, 37795, 8967, 1530, 195, 18, 1; ...
%e A135902 where column 0 of T^3 = column 2 of T = column 0 of T shift left;
%e A135902 also, column 1 of T^3 = column 2 of T^2.
%o A135902 (PARI) T(n, k)=if(k>n || n<0 || k<0, 0, if(k==n,1,if(k==0, T(n+1,2), sum(j=0, n-k, T(n-k, j)*T(j+k-1, k-1))); ); )
%Y A135902 Cf. columns: A135903, A135904, A135905; variants: A091351, A094587.
%K A135902 nonn,tabl
%O A135902 0,4
%A A135902 _Paul D. Hanna_, Dec 18 2007