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%I #19 Oct 10 2023 07:57:52
%S 1,3,7,8,0,1,0,7,0,8,4,6,5,5,4,6,4,2,8,4,5,3,8,6,1,3,1,4,0,2,1,9,3,8,
%T 4,3,0,8,4,5,2,2,5,4,1,2,3,2,6,2,5,9,8,2,6,8,3,9,3,7,0,0,3,7,0,9,2,4,
%U 8,6,3,1,0,7,7,3,1,8,1,7,0,4,8,9,3,6,2,9,1,7,6,9,8,5,9,2,4,3,4,4,1,4
%N Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k)^5 dx.
%H Vaclav Kotesovec, <a href="http://oeis.org/A258232/a258232_2.pdf">The integration of q-series</a>
%F Sum_{m = -infinity..infinity} (Sum_{h = -infinity..infinity} (2*Pi*(-1)^(h+m) / cosh(sqrt(7 - 4*h + 12*h^2 - 4*m + 12*m^2)*Pi/2))). - _Vaclav Kotesovec_, Dec 04 2015
%e 0.137801070846554642845386131402193843084522541232625982683937003709248631...
%p evalf(Sum(Sum(2*Pi*(-1)^(h+m) / cosh(sqrt(7 - 4*h + 12*h^2 - 4*m + 12*m^2)*Pi/2), m=-infinity..infinity), h=-infinity..infinity), 120); # _Vaclav Kotesovec_, Dec 04 2015
%t nmax=200; p=1; q5=Table[PrintTemporary[n]; p=Expand[p*(1-x^n)^5]; Total[CoefficientList[p,x]/Range[1,Exponent[p,x]+1]],{n,1,nmax}]; q5n=N[q5,1000]; Table[SequenceLimit[Take[q5n,j]],{j,Length[q5n]-100,Length[q5n],10}]
%t nterms = 40; N[Sum[Sum[2*Pi*(-1)^(h+m) / Cosh[Sqrt[7 - 4*h + 12*h^2 - 4*m + 12*m^2]*Pi/2], {m, -nterms, nterms}], {h, -nterms, nterms}], 100] (* _Vaclav Kotesovec_, Dec 04 2015 *)
%t RealDigits[NIntegrate[QPochhammer[x]^5, {x, 0, 1}, WorkingPrecision -> 120], 10, 106][[1]] (* _Vaclav Kotesovec_, Oct 10 2023 *)
%Y Cf. A000728, A258232, A258406, A258407, A258404, A258405.
%K nonn,cons
%O 0,2
%A _Vaclav Kotesovec_, May 29 2015
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