OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..86
Vaclav Kotesovec, Asymptotic of sequences A244820, A244821 and A244822
FORMULA
O.g.f.: Sum_{n>=0} x^n/(1 - n*3^n*x)^(n+1).
a(n) = Sum_{k=0..n} C(n,k) * k^(n-k) * 3^(k*(n-k)).
EXAMPLE
E.g.f.: A(x) = 1 + x + 7*x^2/2! + 82*x^3/3! + 2377*x^4/4! + 125956*x^5/5! +...
where
A(x) = 1 + exp(3*x)*x + exp(3^2*x)^2*x^2/2! + exp(3^3*x)^3*x^3/3! + exp(3^4*x)^4*x^4/4! + exp(3^5*x)^5*x^5/5! + exp(3^6*x)^6*x^6/6! +...
MAPLE
N:= 31:
S:= series(add(exp(n*3^n*x)*x^n/n!, n=0..N), x, N):
seq(coeff(S, x, j)*j!, j=0..N-1); # Robert Israel, Jul 04 2017
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*k^(n-k)*3^(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) * 3^(k*(n-k)) )
for(n=0, 25, print1(a(n), ", "))
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp(k*3^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*3^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