A182926 Row sums of absolute values of A182928.

1, 2, 3, 10, 25, 161, 721, 5706, 40881, 385687, 3628801, 41268613, 479001601, 6324319717, 87212177053, 1317906346186, 20922789888001, 357099708702023, 6402373705728001, 121882752536893635, 2432928081076384321, 51140835669924352717

Offset

1,2

Comments

The sum of multinomial coefficients can be computed recursively as

A005651(0) = 1 and A005651(n) = Sum_{1<=k<=n} binomial(n-1,k-1) * A182926(k) * A005651(n-k).

Möbius inversion yields: 1, 1, 2, 8, 24, 157, 720, 5696, 40878,...

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

Links

Seiichi Manyama, Table of n, a(n) for n = 1..450

Formula

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

E.g.f.: Sum_{k>=1} log(1/(1 - x^k/k!)). - Ilya Gutkovskiy, May 21 2019

Example

a(6) = 1 + 10 + 30 + 120 = 161.

Maple

A182926 := proc(n) local d;
add(n!/(d*((n/d)!)^d), d = numtheory[divisors](n)) end:
seq(A182926(i), i = 1..22);

Mathematica

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

Crossrefs

Cf. A182927, A182928, A005651, A007837.

Sequence in context: A378424 A005158 A370608 * A005225 A211208 A303836

Adjacent sequences: A182923 A182924 A182925 * A182927 A182928 A182929

Keyword

nonn

Author

Peter Luschny, Apr 16 2011

Status

approved