OFFSET
0,5
COMMENTS
Here sigma(n,n) = A023887(n), the sum of the n-th powers of the divisors of n.
Compare to: exp( Sum_{n>=1} sigma(n)*x^n/n ), the g.f. of the partitions.
FORMULA
a(n) == 1 (mod 30) (conjecture - valid up to n=4000; if true for n>=0, why?).
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + 31*x^4/4! + 151*x^5/5! + 451*x^6/6! +...
where
log(A(x)) = x + 5*x^4/2^2 + 28*x^9/3^3 + 273*x^16/4^4 + 3126*x^25/5^5 + 47450*x^36/6^6 + 823544*x^49/7^7 +...+ A023887(n)*x^(n^2)/n^n +...
PROG
(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, sigma(m, m)*(x^m/m)^m)+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 20 2013
STATUS
approved