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A131631
Supersubfactorials: partial product of positive subfactorials (A000166).
1
1, 2, 18, 792, 209880, 389117520, 5771780174160, 770509566129663360, 1028600220910021528728960, 15104551945968674840127424147200, 2661646219535110627933754465838408595200
OFFSET
2,2
COMMENTS
This is to subfactorials (A000166, rencontres numbers, or derangements) as superfactorials (A000178) are to factorials (A000142).
FORMULA
a(n) = Product_{k=2..n} A000166(k).
a(n) ~ c * n^(n^2/2 + n + 5/12) * (2*Pi)^((n+1)/2) / (A * exp(3*n^2/4 + 2*n - 13/12)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and c = 1.2517384488693662195086340541087053383189277225386098721341690164735... . - Vaclav Kotesovec, Jul 11 2015
EXAMPLE
a(2) = 1.
a(3) = 1 * 2 = 2.
a(4) = 1 * 2 * 9 = 18 = 2 * 3^2.
a(5) = 1 * 2 * 9 * 44 = 792 = 2^3 * 3^2 * 11.
a(6) = 1 * 2 * 9 * 44 * 265 = 209880 = 2^3 * 3^2 * 5 * 11 * 53.
a(7) = 1 * 2 * 9 * 44 * 265 * 1854 = 389117520 = 2^4 * 3^4 * 5 * 11 * 53 * 103.
MATHEMATICA
Table[Product[k!*Sum[(-1)^j/j!, {j, 0, k}], {k, 2, n}], {n, 2, 15}] (* Vaclav Kotesovec, Jul 11 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 01 2007
STATUS
approved