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A182926 Row sums of absolute values of A182928. 3
1, 2, 3, 10, 25, 161, 721, 5706, 40881, 385687, 3628801, 41268613, 479001601, 6324319717, 87212177053, 1317906346186, 20922789888001, 357099708702023, 6402373705728001, 121882752536893635, 2432928081076384321, 51140835669924352717 (list; graph; refs; listen; history; text; internal format)
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

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

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: A246437 A341265 A005158 * A005225 A211208 A303836

Adjacent sequences:  A182923 A182924 A182925 * A182927 A182928 A182929

KEYWORD

nonn

AUTHOR

Peter Luschny, Apr 16 2011

STATUS

approved

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Last modified June 18 18:17 EDT 2021. Contains 345120 sequences. (Running on oeis4.)