OFFSET
1,2
LINKS
Jonathan Burns and Tilahun Muche, Counting Irreducible Double Occurrence Words, arXiv preprint arXiv:1105.2926 [math.CO], 2011.
FORMULA
Theorem 3.3 of Burns-Muche gives a recurrence.
MAPLE
A047974 := proc(n) option remember; if n= 1 then 1; elif n=2 then 3; else procname(n-1)+2*(n-1)*procname(n-2) ; end if; end proc:
A195186 := proc(n) if n <= 1 then 1; else A047974(n)-add(procname(n-2*k)*doublefactorial(2*k-1), k=1..floor(n/2)) ; end if; end proc:
seq(A195186(n), n=1..20) ; # R. J. Mathar, Sep 12 2011
MATHEMATICA
b[n_] := Sum[Binomial[k, n - k]*(n!/k!), {k, 0, n}];
a[1] = 1; a[n_] := b[n] - Sum[a[n - 2*k]*(2*k - 1)!!, {k, 1, n/2}];
Array[a, 20] (* Jean-François Alcover, Nov 29 2017, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 10 2011
STATUS
approved