A132961 - OEIS

%I #12 Oct 11 2017 21:06:51

%S 1,2,9,38,215,1384,10409,86946,825075,8541998,97590779,1205343952,

%T 16148472977,231416203212,3560209750005,58104163643054,

%U 1008693571819919,18477578835352366,357476371577422955,7258865626801695048,154893910336866444009,3454112338490001478772

%N Total number of all distinct cycle sizes in all permutations of [n].

%H Alois P. Heinz, <a href="/A132961/b132961.txt">Table of n, a(n) for n = 1..450</a>

%F E.g.f.: 1/(1-x)*Sum_{k>0} (1-exp(-x^k/k)). Exponential convolution of A132960(n) and n!: a(n) = n!*Sum_{k=1..n} A132960(k)/k!.

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,

%p       add(multinomial(n, n-i*j, i$j)/j!*(i-1)!^j*(p-> p+

%p       [0, p[1]*`if`(j>0, 1, 0)])(b(n-i*j, i-1)), j=0..n/i)))

%p     end:

%p a:= n-> b(n$2)[2]:

%p seq(a(n), n=1..30);  # _Alois P. Heinz_, Oct 21 2015

%t Rest[ Range[0, 21]! CoefficientList[ Series[1/(1 - x) Sum[1 - Exp[ -x^k/k], {k, 25}], {x, 0, 21}], x]] - _Robert G. Wilson v_, Sep 13 2007

%Y Cf. A000254, A132958, A132959, A132960, A132962, A132963.

%Y Row sums of A293211.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, Sep 06 2007

%E More terms from _Robert G. Wilson v_, Sep 13 2007