A256105 - OEIS

%I #6 Mar 14 2015 12:12:37

%S 1,2,10,36,166,556,2724,9000,41542,153164,657644,2325816,11020508,

%T 38006264,164662664,634362320,2695771462,9775537676,43527018396,

%U 156855914904,687387270260,2605392165928,10799896586616,40214700074800,178809945153820,657023566793400

%N a(n) = [x^n] 2^(2*n) / Product_{k>=1} (1-x^k)^(2^(-k)).

%C Limit n->infinity a(n)^(1/n) = 4.

%H Vaclav Kotesovec, <a href="/A256105/b256105.txt">Table of n, a(n) for n = 0..500</a>

%H Vaclav Kotesovec, <a href="/A256105/a256105.jpg">Graph a(n)/4^n</a>

%t Table[2^(2*n) * SeriesCoefficient[Product[1/(1-x^k)^(2^(-k)),{k,1,n}],{x,0,n}], {n,0,30}]

%t Table[4^n * (CoefficientList[Series[Exp[Sum[x^k/(2*k*(1-x^k/2)),{k,1,n}]],{x,0,n}],x])[[n+1]],{n,0,30}] (* faster *)

%Y Cf. A034899, A144074.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Mar 14 2015