OFFSET
0,2
COMMENTS
Compare to g.f. of A010054:
exp( Sum_{n>=1} x^n/(1 + x^n)/n ) = 1 + x + x^3 + x^6 + x^10 +...
FORMULA
G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} -(-1)^d * 2^(n^2/d) * d ). - Paul D. Hanna, Oct 02 2015
Logarithmic derivative equals A262826.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 6*x^2 + 188*x^3 + 16614*x^4 + 6744492*x^5 +...
where
log(A(x)) = 2/(1 + 2*x)*x + 2^4/(1 + 2^4*x^2)*x^2/2 + 2^9/(1 + 2^9*x^3)*x^3/3 + 2^16/(1 + 2^16*x^4)*x^4/4 + 2^25/(1 + 2^25*x^5)*x^5/5 +...
Explicitly,
log(A(x)) = 2*x + 8*x^2/2 + 536*x^3/3 + 64960*x^4/4 + 33554592*x^5/5 + 68718964352*x^6/6 + 562949953422208*x^7/7 +...+ A262826(n)*x^n/n +...
PROG
(PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(k=1, n, x^k/k * 2^(k^2)/(1 + 2^(k^2)*x^k +x*O(x^n)))), n))}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, -(-1)^d * 2^(m^2/d) * d) ) +x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Oct 02 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 26 2009
STATUS
approved