A343542 - OEIS

%I #16 Apr 28 2021 20:54:14

%S 1,0,0,0,0,1,1,1,1,1,1,463,793,3004,5006,14444,23817,62323,14805403,

%T 35175993,177791475,745977222,2333540804,7589340982,29027728612,

%U 81515120641,23232813583331,69799133324911,436678552247551,2215090972333651,13529994077951557,48863594588239153

%N Number of ways to partition n labeled elements into sets of different sizes of at least 5.

%H Alois P. Heinz, <a href="/A343542/b343542.txt">Table of n, a(n) for n = 0..700</a>

%F E.g.f.: Product_{k>=5} (1 + x^k/k!).

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

%p      `if`(i>n, 0, b(n, i+1)+binomial(n, i)*b(n-i, i+1)))

%p     end:

%p a:= n-> b(n, 5):

%p seq(a(n), n=0..31);  # _Alois P. Heinz_, Apr 28 2021

%t nmax = 31; CoefficientList[Series[Product[(1 + x^k/k!), {k, 5, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%t a[0] = 1; a[n_] := a[n] = -(n - 1)! Sum[DivisorSum[k, # (-#!)^(-k/#) &, # > 4 &] a[n - k]/(n - k)!, {k, 1, n}]; Table[a[n], {n, 0, 31}]

%Y Cf. A007837, A025150, A032311, A057814, A245790, A341283, A343319.

%K nonn

%O 0,12

%A _Ilya Gutkovskiy_, Apr 28 2021