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A131631 Supersubfactorials: partial product of positive subfactorials (A000166). 1
1, 2, 18, 792, 209880, 389117520, 5771780174160, 770509566129663360, 1028600220910021528728960, 15104551945968674840127424147200, 2661646219535110627933754465838408595200 (list; graph; refs; listen; history; text; internal format)
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 to 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: A013035 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

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Last modified February 20 15:52 EST 2020. Contains 332078 sequences. (Running on oeis4.)