OFFSET
0,2
COMMENTS
Partial products of A000124.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..269
Spencer J. Franks, Pamela E. Harris, Kimberly Harry, Jan Kretschmann, and Megan Vance, Counting Parking Sequences and Parking Assortments Through Permutations, arXiv:2301.10830 [math.CO], 2023.
FORMULA
a(n) grows roughly like n*(n!)^2/2^n. [Corrected by Vaclav Kotesovec, Mar 18 2023]
G.f.: G(0)/(2*x^2) - 1/x^2 - 1/x, where G(k)= 1 + 1/(1 - x*(k^2-k+2)/(x*(k^2-k+2) + 2/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 18 2013
a(n) = -2^(-n-1)*Gamma(n+3/2+sqrt(-7)/2)*Gamma(n+3/2-sqrt(-7)/2)*sin((3+sqrt(-7))*Pi/2)/Pi. - Robert Israel, May 19 2014
a(n) ~ cosh(sqrt(7)*Pi/2) * n^(2*(n+1)) / (2^n * exp(2*n)). - Vaclav Kotesovec, Mar 18 2023
MAPLE
a[0]:=1:for n from 1 to 20 do a[n]:=product(k*(k+1)/2+1, k=1..n) od: seq(a[n], n=0..20);
MATHEMATICA
FoldList[Times, Accumulate[Range[0, 20]]+1] (* Harvey P. Dale, Apr 21 2024 *)
PROG
(PARI) a(n) = if (n, prod(k=1, n, k*(k+1)/2+1), 1); \\ Michel Marcus, Mar 18 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Miklos Kristof, Apr 10 2007
EXTENSIONS
More terms from Michel Marcus, Mar 18 2023
STATUS
approved