OFFSET
0,4
COMMENTS
Each term divides its successor, as in A203308.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..16
FORMULA
a(n) ~ c * (2*Pi)^(n*(n-1)/4) * n^(n^3/3 + n^2/4 - 7*n/12 - 11/8) / exp(4*n^3/9 - n^2/8 - n), where c = A323720 = 0.29363504888070220142364974947015983077985979... - Vaclav Kotesovec, Jan 25 2019
MAPLE
with(LinearAlgebra):
a:= n-> Determinant(VandermondeMatrix([i!$i=1..n])):
seq(a(n), n=0..10); # Alois P. Heinz, Jul 23 2017
MATHEMATICA
PROG
(Python)
from sympy import factorial, prod
f = factorial
def v(n): return 1 if n<2 else prod(f(k) - f(j) for k in range(2, n + 1) for j in range(1, k))
print([v(n) for n in range(11)]) # Indranil Ghosh, Jul 24 2017
(Magma) F:= Factorial; [1, 1] cat [(&*[(&*[F(k+1) - F(j): j in [1..k]]): k in [1..n-1]]): n in [2..20]]; // G. C. Greubel, Aug 30 2023
(SageMath) f=factorial; [product(product(f(k+1) - f(j) for j in range(1, k+1)) for k in range(1, n)) for n in range(21)] # G. C. Greubel, Aug 30 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 01 2012
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jul 23 2017
Offset corrected by Vaclav Kotesovec, Jan 25 2019
STATUS
approved