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A195186
Number of palindromic double occurrence words of length 2n.
1
1, 2, 6, 20, 72, 290, 1198, 5452, 25176, 125874, 637926, 3448708, 18919048, 109412210, 642798510, 3945170012, 24614491704, 159328958690, 1048645656646, 7122719571700, 49185991168968, 349097516604738, 2518145666958126, 18609525157571692, 139704193446510616
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
Sequence in context: A154381 A150135 A150136 * A150137 A150138 A148481
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 10 2011
STATUS
approved