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A258566 Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order.

%I A258566 #25 Feb 08 2024 17:39:44
%S A258566 1,3,2,15,10,6,105,70,42,30,1155,770,462,330,210,15015,10010,6006,
%T A258566 4290,2730,2310,255255,170170,102102,72930,46410,39270,30030,4849845,
%U A258566 3233230,1939938,1385670,881790,746130,570570,510510
%N A258566 Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order.
%C A258566 Triangle read by rows, truncated rows of the array in A185973.
%C A258566 Reversal of A077011.
%F A258566 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 A258566 Triangle begins:
%e A258566       1;
%e A258566       3,     2;
%e A258566      15,    10,    6;
%e A258566     105,    70,   42,   30;
%e A258566    1155,   770,  462,  330,  210;
%e A258566   15015, 10010, 6006, 4290, 2730, 2310;
%e A258566   ...
%p A258566 T:= n-> (m-> seq(m/ithprime(j), j=1..n))(mul(ithprime(i), i=1..n)):
%p A258566 seq(T(n), n=1..10);  # _Alois P. Heinz_, Jun 18 2015
%t A258566 T[1, 1] = 1; T[n_, n_] := T[n, n] = Prime[n-1]*T[n-1, n-1];
%t A258566 T[n_, k_] := T[n, k] = Prime[n]*T[n-1, k];
%t A258566 Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, May 26 2016 *)
%Y A258566 Row sums: A024451.
%Y A258566 T(n,1) = A070826(n).
%Y A258566 T(n,n) = A002110(n-1).
%Y A258566 For 2 <= n <= 9, T(n,2) = A118752(n-2). [corrected by _Peter Munn_, Jan 13 2018]
%Y A258566 T(n,k) = A121281(n,k), but the latter has an extra column (0).
%Y A258566 Cf. A077011, A185973, A286947.
%K A258566 nonn,tabl
%O A258566 1,2
%A A258566 _Philippe Deléham_, Jun 03 2015