A092144 a(n) = A092143(n)/n!.

1, 1, 1, 2, 2, 12, 12, 96, 288, 2880, 2880, 414720, 414720, 5806080, 87091200, 5573836800, 5573836800, 1805923123200, 1805923123200, 722369249280000, 15169754234880000, 333734593167360000, 333734593167360000, 4613547015945584640000, 23067735079727923200000

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..200

Mathematica

Table[Product[k^Floor[n/k], {k, n}]/n!, {n, 40}] (* G. C. Greubel, Feb 05 2024 *)

Prog

(PARI) my(z=1); for(i=1, 20, fordiv(i, j, z*=j); print1(z/i!, ", "))
(Magma) [(&*[j^Floor(n/j): j in [1..n]])/Factorial(n): n in [1..40]]; // G. C. Greubel, Feb 05 2024
(SageMath) [product(j^(n//j) for j in range(1, n+1))//factorial(n) for n in range(1, 41)] # G. C. Greubel, Feb 05 2024
(Python)
from math import factorial
def A092144(n):
    c, j = 1, 1
    while j <= n:
        c *= factorial(k:=n//j)**(-j-(j==1)+(j:=n//k+1))
    return c # Chai Wah Wu, Jun 27 2026

Crossrefs

Cf. A092143.

Sequence in context: A334958 A205957 A341432 * A224497 A305753 A181813

Adjacent sequences: A092141 A092142 A092143 * A092145 A092146 A092147

Keyword

nonn,changed

Author

Jon Perry, Mar 31 2004

Extensions

Terms a(21) onward added by G. C. Greubel, Feb 05 2024

Status

approved