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%I #10 May 09 2014 10:13:04
%S 1,1,5,35,355,4465,69125,1252475,26151475,616872025,16234589525,
%T 471382586675,14970245087875,516142537458625,19199498482905125,
%U 766394702651760875,32676482018991377875,1482055899582130035625,71248344993651091083125,3618867148116847594611875
%N E.g.f. satisfies: A'(x) = Product_{n>=1} 1/(1 - A(x)^n), where A(0) = 0.
%C CONJECTURES.
%C a(n) == 1 (mod 2).
%C a(n) == 0 (mod 5^k) for n >= 5*k-2.
%C a(n) == 0 (mod 7^k) for n >= 7*k.
%H Vaclav Kotesovec, <a href="/A233860/b233860.txt">Table of n, a(n) for n = 1..380</a>
%F E.g.f.: Series_Reversion( Integral eta(x) dx ), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor.
%F E.g.f. A(x) satisfies: log(A'(x)) = Sum_{n>=1} sigma(n)*A(x)^n/n.
%e 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! +...
%e where
%e A'(x) = 1/( (1 - A(x)) * (1 - A(x)^2) * (1 - A(x)^3) * (1 - A(x)^4) * (1 - A(x)^5) *...).
%o (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)}
%o for(n=1, 30, print1(a(n), ", "))
%o (PARI) {a(n)=local(A=serreverse(intformal(eta(x+x*O(x^n))))); n!*polcoeff(A,n)}
%o for(n=1, 30, print1(a(n), ", "))
%Y Cf. A233861.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Dec 16 2013
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