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.

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.

Links

Table of n, a(n) for n=0..44.

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

Cf. A007318, A008578, A360208.

Sequence in context: A286121 A285537 A285781 * A228245 A034078 A180011

Adjacent sequences: A360204 A360205 A360206 * A360208 A360209 A360210

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 30 2023

Status

approved