OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
FORMULA
a(n) = Sum_{k=0..n} C(n,k)*[k*(k-1)]^(n-k).
O.g.f.: Sum_{n>=0} x^n/(1 - n*(n-1)*x)^(n+1). - Paul D. Hanna, Jul 30 2014
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*(k*(k - 1))^(n - k), {k, 0, n}], {n, 1, 25}]}] (* G. C. Greubel, Nov 05 2016 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(k*(k-1))^(n-k))}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(k*(k-1)*x +x*O(x^n))*x^k/k!), n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) /* From Sum_{n>=0} x^n/(1 - n*(n-1)*x)^(n+1): */
{a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k-1)*x +x*O(x^n))^(k+1)), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 27 2007
STATUS
approved