OFFSET
1,3
COMMENTS
CONJECTURES.
a(n) == 1 (mod 2).
a(n) == 0 (mod 5^k) for n >= 5*k-2.
a(n) == 0 (mod 7^k) for n >= 7*k.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..380
FORMULA
E.g.f.: Series_Reversion( Integral eta(x) dx ), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor.
E.g.f. A(x) satisfies: log(A'(x)) = Sum_{n>=1} sigma(n)*A(x)^n/n.
EXAMPLE
E.g.f. A(x) = x + x^2/2! + 5*x^3/3! + 35*x^4/4! + 355*x^5/5! + 4465*x^6/6! +...
where
A'(x) = 1/( (1 - A(x)) * (1 - A(x)^2) * (1 - A(x)^3) * (1 - A(x)^4) * (1 - A(x)^5) *...).
PROG
(PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(1/prod(k=1, n, 1-A^k+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
(PARI) {a(n)=local(A=serreverse(intformal(eta(x+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 16 2013
STATUS
approved