A131631 Supersubfactorials: partial product of positive subfactorials (A000166).

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).

Links

Table of n, a(n) for n=2..12.

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

Cf. A000142, A000166, A000178.

Sequence in context: A350008 A132520 A297707 * A306789 A015190 A180606

Adjacent sequences: A131628 A131629 A131630 * A131632 A131633 A131634

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 01 2007

Status

approved