A397838 Antidiagonal products of the multifactorial array.

1, 1, 2, 12, 144, 5760, 259200, 58060800, 9144576000, 5618427494400, 4147979673600000, 8009630236016640000, 7588811772444672000000, 87964963104029147136000000, 287964353346502458802176000000, 2259278037969787970377482240000000, 30746913887983889201171005440000000000

Offset

0,3

Comments

It appears that the only squares in this sequence are a(0) = a(1) = 1, a(4) = 144, a(18) = 14671475874842562153331362760375664640000000000.

Links

Table of n, a(n) for n=0..16.

Eric Weisstein's World of Mathematics, Multifactorial.

Formula

a(n) = Product_{k=1..n+1} A(n+1-k, k), where A denotes one of the arrays A114423 and A129116.

a(n) = Product_{k=1..n} Product_{m=1..floor(n/k)} (n + 1 - m*k).

Mathematica

A[0, k_]:=1; A[n_, k_]:=A[n, k]=If[1 <= n <= k, n, n*A[n - k, k]]; a[n_]:=Product[A[n+1-k, k], {k, n+1}]; Array[a, 17, 0]
(* Alternative: *)
a[n_]:=Product[Product[n+1-m*k, {m, Floor[n/k]}], {k, n}]; Array[a, 17, 0]

Crossrefs

Cf. A000290, A010766, A114423, A129116.

Sequence in context: A221101 A385630 A187748 * A324140 A296137 A086928

Adjacent sequences: A397834 A397835 A397837 * A397840 A397843 A397847

Keyword

nonn,new

Author

Stefano Spezia, Jul 12 2026

Status

approved