%I #25 Feb 08 2024 17:39:44
%S 1,3,2,15,10,6,105,70,42,30,1155,770,462,330,210,15015,10010,6006,
%T 4290,2730,2310,255255,170170,102102,72930,46410,39270,30030,4849845,
%U 3233230,1939938,1385670,881790,746130,570570,510510
%N Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order.
%C Triangle read by rows, truncated rows of the array in A185973.
%C Reversal of A077011.
%F T(1,1) = 1, T(n,k) = A000040(n)*T(n-1,k) for k < n, T(n,n) = A000040(n-1) * T(n-1,n-1).
%e Triangle begins:
%e 1;
%e 3, 2;
%e 15, 10, 6;
%e 105, 70, 42, 30;
%e 1155, 770, 462, 330, 210;
%e 15015, 10010, 6006, 4290, 2730, 2310;
%e ...
%p T:= n-> (m-> seq(m/ithprime(j), j=1..n))(mul(ithprime(i), i=1..n)):
%p seq(T(n), n=1..10); # _Alois P. Heinz_, Jun 18 2015
%t T[1, 1] = 1; T[n_, n_] := T[n, n] = Prime[n-1]*T[n-1, n-1];
%t T[n_, k_] := T[n, k] = Prime[n]*T[n-1, k];
%t Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, May 26 2016 *)
%Y Row sums: A024451.
%Y T(n,1) = A070826(n).
%Y T(n,n) = A002110(n-1).
%Y For 2 <= n <= 9, T(n,2) = A118752(n-2). [corrected by _Peter Munn_, Jan 13 2018]
%Y T(n,k) = A121281(n,k), but the latter has an extra column (0).
%Y Cf. A077011, A185973, A286947.
%K nonn,tabl
%O 1,2
%A _Philippe Deléham_, Jun 03 2015