OFFSET
0,3
COMMENTS
a(n) = A186766(n,0).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
FORMULA
E.g.f.: g(z) = exp(sinh z)/sqrt(1-z^2).
EXAMPLE
a(3)=5 because we have (1)(2)(3), (1)(23), (12)(3), (13)(2), and (123).
MAPLE
g := exp(sinh(z))/sqrt(1-z^2): gser := series(g, z = 0, 27): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 21);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
binomial(n-1, j-1)*`if`(j::even, (j-1)!, 1), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Apr 13 2017
MATHEMATICA
a[n_] := a[n] = If[n==0, 1, Sum[a[n-j]*Binomial[n-1, j-1]*If[EvenQ[j], (j-1)!, 1], {j, 1, n}]];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 18 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 27 2011
STATUS
approved