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

Author

Peter Luschny, Apr 16 2011

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

Cf. A182927, A182928, A005651, A007837.

Programs

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 *)

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