OFFSET
0,3
EXAMPLE
O.g.f.: A(x) = 1 + x + 3*x^2 + 28*x^3 + 427*x^4 + 9096*x^5 + 248298*x^6 +...
where
A(x) = 1 + 1^1*2^0*exp(-1*2*x/A(x))*x/A(x) + 2^2*3^1*exp(-2*3*x/A(x))*x^2/A(x)^2/2! + 3^3*4^2*exp(-3*4*x/A(x))*x^3/A(x)^3/3! + 4^4*5^3*exp(-4*5*x/A(x))*x^4/A(x)^4/4! + 5^5*6^4*exp(-5*6*x)*x^5/A(x)/5! +...
PROG
(PARI) {a(n)=local(A=1); for(i=1, n, A=sum(m=0, n, m^m*(m+1)^(m-1)*(x/A)^m*exp(-m*(m+1)*x/A+x*O(x^n))/m!)); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 21 2012
STATUS
approved