OFFSET
1,1
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..64
Steve Butler, Persi Diaconis and R. L. Graham, The mathematics of the flip and horseshoe shuffles, arXiv:1412.8533 [math.CO], 2014.
Steve Butler, Persi Diaconis and R. L. Graham, The mathematics of the flip and horseshoe shuffles, The American Mathematical Monthly 123.6 (2016): 542-556.
FORMULA
See Maple program.
MAPLE
f:=proc(n) local k, i, np;
if n=1 then 2
elif n=2 then 12
elif n=3 then 120
elif n=6 then 12!/7!
elif (n mod 2) = 1 then (2*n)!
else
np:=n; k:=1;
for i while (np mod 2) = 0 do
np:=np/2; k:=k+1; od;
if (n=2^(k-1)) then (k+1)*2^k else (2*n)!/2; fi;
fi;
end;
[seq(f(n), n=1..64)];
MATHEMATICA
a[n_] := Which[n == 1, 2, n == 2, 12, n == 3, 120, n == 6, 12!/7!, OddQ[n], (2 n)!, True, np = n; k = 1; While[EvenQ[np], np = np/2; k++]; If[n == 2^(k - 1), (k + 1)*2^k, (2n)!/2]];
Array[a, 17] (* Jean-François Alcover, Nov 30 2017, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 20 2016
STATUS
approved