OFFSET
3,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..145
FORMULA
a(n) ~ c * n^(n-2), where c = 0.130848879059... . - Vaclav Kotesovec, Sep 07 2014
EXAMPLE
a(4) = 6:
.1-2. .1 2. .1 2. .1 2. .1 2. .1 2.
. . . |. . . .| . . \ . . / .
.4 3. .4 3. .4-3. .4 3. .4 3. .4 3.
MAPLE
T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
`if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
`if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
end:
a:= n-> T(n, 3):
seq(a(n), n=3..25);
MATHEMATICA
T[n_, k_] := T[n, k] = If[k<0 || k>n, 0, If[n == 0, 1, Sum[Binomial[n-1, i]*T[n-1-i, k-1]*If[i<2, 1, i!/2 + (i+1)^(i-1)], {i, 0, n-k}]]];
a[n_] := T[n, 3];
Table[a[n], {n, 3, 25}] (* Jean-François Alcover, Apr 01 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 25 2012
STATUS
approved