OFFSET
0,3
LINKS
FORMULA
O.g.f.: Sum_{n>=0} x^n/(1 - n*4^n*x)^(n+1).
a(n) = Sum_{k=0..n} C(n,k) * k^(n-k) * 4^(k*(n-k)).
EXAMPLE
E.g.f.: A(x) = 1 + x + 9*x^2/2! + 145*x^3/3! + 7169*x^4/4! + 702721*x^5/5! +...
where
A(x) = 1 + exp(4*x)*x + exp(4^2*x)^2*x^2/2! + exp(4^3*x)^3*x^3/3! + exp(4^4*x)^4*x^4/4! + exp(4^5*x)^5*x^5/5! + exp(4^6*x)^6*x^6/6! +...
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*k^(n-k)*4^(k*(n-k)), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jul 11 2014 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(n, k) * k^(n-k) * 4^(k*(n-k)) )}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(k*4^k*x +x*O(x^n))*x^k/k!), n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-k*4^k*x +x*O(x^n))^(k+1)), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 06 2014
STATUS
approved