A195186 Number of palindromic double occurrence words of length 2n.

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

Table of n, a(n) for n=1..25.

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

Adjacent sequences: A195183 A195184 A195185 * A195187 A195188 A195189

Keyword

nonn

Author

N. J. A. Sloane, Sep 10 2011

Status

approved