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A182927 Row sums of A182928. 3
1, 0, 3, -8, 25, -99, 721, -5704, 40881, -340325, 3628801, -41245511, 479001601, -6129725315, 87212177053, -1317906346184, 20922789888001, -354320889234597, 6402373705728001, -121882630320799633, 2432928081076384321, -51041048673495232715 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The number of partitions of an n-set with distinct block sizes can

be computed recursively as A007837(0) = 1 and A007837(n) = - Sum_{1<=k<=n} binomial(n-1,k-1) * A182927(k) * A007837(n-k).

Möbius inversion yields: 1, -1, 2, -8, 24, -101, 720, -5696, 40878,...

A182927(2*i+1) = A182926(2*i+1)

LINKS

Table of n, a(n) for n=1..22.

FORMULA

a(n) = Sum_{d|n} -n!/(d*(-(n/d)!)^d).

EXAMPLE

a(6) = 1 - 10 + 30 - 120 = -99.

MAPLE

A182927 := proc(n) local d;

add(-n! / (d*(-(n/d)!)^d), d = numtheory[divisors](n)) end:

seq(A182927(i), i = 1..22);

MATHEMATICA

a[n_] := Sum[ -n!/(d*(-(n/d)!)^d), {d, Divisors[n]}]; Table[a[n], {n, 1, 22}] // Flatten (* Jean-François Alcover, Jul 29 2013 *)

CROSSREFS

Cf. A182926, A182928, A005651, A007837.

Sequence in context: A006219 A009268 A024430 * A012408 A184325 A051403

Adjacent sequences:  A182924 A182925 A182926 * A182928 A182929 A182930

KEYWORD

sign

AUTHOR

Peter Luschny, Apr 16 2011

STATUS

approved

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Last modified September 20 12:31 EDT 2017. Contains 292271 sequences.