OFFSET
0,3
COMMENTS
More generally, if G(x) = exp(x*exp(x*G(x)^p)),
where G(x)^m = Sum_{n>=0} g(n,m)*x^n/n!,
then g(n,m) = Sum_{k=0..n} C(n,k) * m*(p*(n-k) + m)^(k-1) * k^(n-k).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..355
FORMULA
a(n) = Sum_{k=0..n} C(n,k) * (3*(n-k) + 1)^(k-1) * k^(n-k).
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 365*x^4/4! +...
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*(3*(n - k) + 1)^(k - 1)*k^(n - k), {k, 0, n}], {n, 1, 50}]}] (* G. C. Greubel, Nov 18 2017 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(3*(n-k)+1)^(k-1)*k^(n-k))}
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=exp(x*exp(x*A^3+O(x^n)))); n!*polcoeff(A, n, x)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 14 2009
STATUS
approved