OFFSET
1,6
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..300
FORMULA
a(n) ~ n! / n^3. - Vaclav Kotesovec, Nov 23 2014
MATHEMATICA
Table[Sum[(-1)^k * k*(k-1)/2 * Sum[Sum[Binomial[k-1, p] * Binomial[k-p-1, i-2*p] * Binomial[n-2*k+p-1, n-3*k+i-1] * (n-3*k+i)!, {p, 0, k-1}], {i, Max[0, 3*k-n], 2*(k-1)}], {k, 2, n-3}], {n, 1, 20}] (* Vaclav Kotesovec, Nov 23 2014 after Tani Akinari *)
PROG
(PARI) a(n)=sum(k=2, n-3, (-1)^k*k*(k-1)/2*sum(i=max(0, 3*k-n), 2*(k-1), sum(p=0, k-1, binomial(k-1, p)*binomial(k-p-1, i-2*p)*binomial(n-2*k+p-1, n-3*k+i-1)*(n-3*k+i)!)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Tani Akinari, Nov 21 2014
STATUS
approved