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%I #3 Oct 03 2015 14:30:54
%S 1,3,36,6687,10778724,169490235888,25016281203451185,
%T 34185693515006540036988,429210580094320740939492003864,
%U 49269611092414637899756996954236224964,51537752221009977969797967261567868189156062717,490093718313094497196906721743434604298698182091562669412,42294065506171581216310316433524563489152717911911865589940031127588
%N G.f.: exp( Sum_{n>=1} x^n/n * 3^(n^2)/(1 + 3^(n^2)*x^n) ).
%C Compare to g.f. of A010054:
%C exp( Sum_{n>=1} x^n/(1 + x^n)/n ) = 1 + x + x^3 + x^6 + x^10 +...
%F G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} -(-1)^d * 3^(n^2/d) * d ).
%e G.f.: A(x) = 1 + 3*x + 36*x^2 + 6687*x^3 + 10778724*x^4 + 169490235888*x^5 +...
%e where
%e log(A(x)) = 3*x/(1 + 3*x) + 3^4/(1 + 3^4*x^2)*x^2/2 + 3^9/(1 + 3^9*x^3)*x^3/3 + 3^16/(1 + 3^16*x^4)*x^4/4 + 3^25/(1 + 3^25*x^5)*x^5/5 +...
%e Explicitly,
%e log(A(x)) = 3*x + 63*x^2/2 + 19764*x^3/3 + 43033275*x^4/4 + 847288610658*x^5/5 + 150094634523748092*x^6/6 + + 239299329230617529605392*x^7/7 +...
%o (PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(k=1, n, x^k/k * 3^(k^2)/(1 + 3^(k^2)*x^k +x*O(x^n)))), n))}
%o for(n=0, 20, print1(a(n), ", "))
%o (PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, -(-1)^d * 3^(m^2/d) * d) ) +x*O(x^n)), n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A158096.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 03 2015
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