OFFSET
2,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..792
FORMULA
E.g.f.: 1-2*exp(x)+exp(x*(x+4)/2).
a(n) ~ n^(n/2) * exp(-1 + 2*sqrt(n) - n/2) / sqrt(2). - Vaclav Kotesovec, Sep 18 2019
EXAMPLE
a(3) = 12: 1a|2a3b, 1b|2a3b, 1a3b|2a, 1a3b|2b, 1a2b|3a, 1a2b|3b, 1a|2a|3b, 1a|2b|3a, 1b|2a|3a, 1a|2b|3b, 1b|2a|3b, 1b|2b|3a.
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)*
binomial(n-1, j-1)*binomial(k, j), j=1..min(k, n)))
end:
a:= n-> (k-> add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(2):
seq(a(n), n=2..27);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k] Binomial[n - 1, j - 1] Binomial[k, j], {j, 1, Min[k, n]}]];
a[n_] := With[{k = 2}, Sum[b[n, k - i] (-1)^i Binomial[k, i], {i, 0, k}]];
a /@ Range[2, 27] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 06 2019
STATUS
approved