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Expansion of A007245^6.
10

%I #28 Jul 15 2017 19:16:52

%S 1,1488,947304,335950912,72474624276,9790124955552,833107628914688,

%T 45630592148400000,1754954450906393538,51062104386000089648,

%U 1186840963302480101376,22924552119951492244800,378933532779364657975000

%N Expansion of A007245^6.

%H Vaclav Kotesovec, <a href="/A028515/b028515.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Seiichi Manyama)

%F a(n) ~ exp(4*Pi*sqrt(2*n)) / (2^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2017

%F (q*j(q))^2 where j(q) is the elliptic modular invariant. - _Seiichi Manyama_, Jul 15 2017

%t CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^6, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jun 29 2017 *)

%Y Cf. A000521 (j(q)).

%Y (q*j(q))^(k/24): A289397 (k=-1), A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12), A028512 (k=16), A028513 (k=32), A028514 (k=40), this sequence (k=48), A288846 (k=72).

%K nonn

%O 0,2

%A _N. J. A. Sloane_