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%I #18 Feb 10 2024 04:40:37
%S 1,3,8,68,2106,223776,80532200,98945392200,421225839051260,
%T 6310402120912239968,337401124757628967733136,
%U 65171905481441631827737564000,45944096973025484590366745753166436
%N a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2^k,n).
%H G. C. Greubel, <a href="/A134173/b134173.txt">Table of n, a(n) for n = 0..59</a>
%F G.f.: Sum_{n>=0} log(1+(2^n+1)*x)^n/n!.
%F From _Vaclav Kotesovec_, Jul 02 2016: (Start)
%F a(n) ~ binomial(2^n,n).
%F a(n) ~ 2^(n^2) / n!.
%F a(n) ~ 2^(n^2 - 1/2) * exp(n) / (sqrt(Pi) * n^(n+1/2)).
%F (End)
%p a:=proc(n) options operator, arrow: sum(binomial(n,k)*binomial(2^k,n),k=0..n) end proc: seq(a(n),n=0..13); # _Emeric Deutsch_, Jan 27 2008
%t Table[Sum[Binomial[n,k]*Binomial[2^k,n],{k,0,n}],{n,0,15}] (* _Vaclav Kotesovec_, Jul 02 2016 *)
%o (PARI) for(n=0,25, print1(sum(k=0,n, binomial(n,k)*binomial(2^k,n)), ", ")) \\ _G. C. Greubel_, Mar 21 2017
%K easy,nonn
%O 0,2
%A _Paul D. Hanna_ and _Vladeta Jovovic_, Jan 13 2008
%E More terms from _Emeric Deutsch_, Jan 27 2008
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