OFFSET
0,4
COMMENTS
E.g.f. may be written as: exp( Sum_{n>=1} Product_{k=1..n} x^k/k ).
Sum_{n>=0} a(n)/n! = e^(e-1) = 5.574941524760880...
FORMULA
a(n) == 1 (mod 3) (conjecture - valid up to n=1024; if true for n>=0, why?).
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 13*x^4/4! + 31*x^5/5! + 271*x^6/6! +...
where
log(A(x)) = x + x^3/2! + x^6/3! + x^10/4! + x^15/5! + x^21/6! + x^28/7! +...
PROG
(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, x^(m*(m+1)/2)/m!)+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 19 2013
STATUS
approved