A222637 Squarefree part of the total number of arrangements of a set with n elements.

1, 2, 5, 1, 65, 326, 1957, 137, 109601, 986410, 9864101, 27126278, 7704505, 16926797486, 236975164805, 888656868019, 56874039553217, 966858672404690, 17403456103284421, 826664164906010, 6613313319248080001, 138879579704209680022, 3055350753492612960485

Offset: 0

Author

Michel Marcus, Feb 27 2013

Keywords

• nonn

Links

• F. Luca and I. E. Shparlinski, On the squarefree parts of floor(e*n!), Glasgow Math. J., 49 (2007), 391-403.

Crossrefs

Cf. A000522, A007913, A222638, A222639.

Programs

Maple

A000522 := proc(n)
    add( n!/k!,k=0..n) ;
end proc:
A222637 := proc(n)
    A007913(A000522(n)) ;
end proc: # R. J. Mathar, Jan 16 2014

Mathematica

core[n_] := Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[n]);
a[n_] := If[n == 0, 1, core[Floor[E*n!]]];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Apr 04 2024 *)

PARI

a(n) = core(n! * polcoeff(exp(x + x*O(x^n)) / (1 - x), n))

Formula

a(n) = core(A000522(n)).