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A360207
Triangular array T(n,k) read by antidiagonals: T(2,1) = 1; otherwise T(n,k) = p(n)!/(p(k)!*p(n-k)!), where p(0)=1 and p(m)=prime(m) for m > 0.
2
1, 1, 1, 1, 1, 1, 1, 10, 10, 1, 1, 21, 140, 21, 1, 1, 3960, 55440, 55440, 3960, 1, 1, 78, 205920, 432432, 205920, 78, 1, 1, 28560, 1485120, 588107520, 588107520, 1485120, 28560, 1, 1, 171, 3255840, 25395552, 4788875520, 25395552, 3255840, 171, 1
OFFSET
0,8
COMMENTS
Essentially analogous to Pascal's triangle, A007318.
FORMULA
T(2,1) = 1; otherwise T(n,k) = p(n)!/(p(k)!*p(n-k)!), where p(0)=1 and p(m)=prime(m) for m > 0.
EXAMPLE
First six rows:
1
1 1
1 1 1
1 10 10 1
1 21 140 21 1
1 3960 55440 55440 3960 1
...
MAPLE
p:= n-> `if`(n=0, 1, ithprime(n)):
T:= (n, k)-> floor(p(n)!/(p(k)!*p(n-k)!)):
seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Jan 30 2023
MATHEMATICA
p[0] = 1; p[n_] := Prime[n];
t = Table[p[n]!/(p[k]!*p[n - k]!), {n, 0, 10}, {k, 0, n}]
t[[3, 2]] = 1;
TableForm[t] (* A360207 array *)
Flatten[t] (* A360207 sequence *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 30 2023
STATUS
approved