%I #9 Nov 05 2019 07:23:52
%S 1,2,-22,364,-6490,124476,-2501116,51848984,-1099502074,23722687340,
%T -518856745492,11473878455400,-256044198076836,5757405060992728,
%U -130302582530068280,2965537736183034672,-67820940980720843322,1557676412999229945932
%N Expansion of g.f.: A(x) = (Sum_{n>=0} (2*n+1)*8^n*x^(n*(n+1)/2))^(1/12).
%H G. C. Greubel, <a href="/A111985/b111985.txt">Table of n, a(n) for n = 0..715</a>
%e G.f.: A(x) = 1 + 2*x - 22*x^2 + 364*x^3 - 6490*x^4 + 124476*x^5 - 2501116*x^6 +...
%e where
%e A(x)^12 = 1 + 3*8*x + 5*8^2*x^3 + 7*8^3*x^6 + 9*8^4*x^10 + 11*8^5*x^15 + 13*8^6*x^21 + 15*8^7*x^28 + 17*8^8*x^36 + 19*8^9*x^45 + 21*8^10*x^55 +...
%p seq(coeff(series( ( add((2*n+1)*8^n*x^(n*(n+1)/2), n=0..40) )^(1/12), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Nov 05 2019
%t CoefficientList[Series[(Sum[(2n+1)*8^n*x^(n(n+1)/2), {n,0,40}])^(1/12), {x,0,30}], x] (* _G. C. Greubel_, Nov 05 2019 *)
%o (PARI) {a(n)=polcoeff(sum(k=0,sqrtint(2*n+1),(2*k+1)*8^k*x^(k*(k+1)/2)+x*O(x^n))^(1/12),n)}
%o (Sage) [( (sum((2*n+1)*8^n*x^(n*(n+1)/2) for n in (0..40)) )^(1/12) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Nov 05 2019
%Y Cf. A111983 (g.f. A(x)^12), A111984 (g.f. A(x)^4).
%K sign
%O 0,2
%A _Paul D. Hanna_, Aug 25 2005