OFFSET
0,2
COMMENTS
T(n,k) is the (k+1)-th product of (n-k) successive primes (k, n-(k+1) >= 0). - Alois P. Heinz, Jan 21 2022
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
T(n,0) = A002110(n); T(n,n) = 1;
T(n,n-1) = A000040(n) for n>0;
T(n,k) = Product_{j=k+1..n} prime(j). - Alois P. Heinz, Jan 21 2022
EXAMPLE
Triangle begins:
1;
2, 1;
6, 3, 1;
30, 15, 5, 1;
210, 105, 35, 7, 1;
...
MAPLE
T:= proc(n, k) option remember;
`if`(n=k, 1, T(n-1, k)*ithprime(n))
end:
seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Jan 21 2022
MATHEMATICA
T[n_, k_] := Times @@ Prime[Range[k + 1, n]];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 13 2021 *)
PROG
(PARI) pr(n) = factorback(primes(n)); \\ A002110
row(n) = my(P=pr(n)); vector(n+1, k, P/pr(k-1)); \\ Michel Marcus, Jan 21 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Aug 03 2004
STATUS
approved