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%I #21 Apr 09 2021 09:37:57
%S 1,3,21,567,67689,33887403,68921796861,563431696713567,
%T 18451249599365935569,2418017680197896730749523,
%U 1267674779574792745831097365221,2658469935859419140387217204140789127,22300777100086187451068223319189800258419769
%N a(n) = Sum_{k=0..n} binomial(n,k)*2^(k^2).
%C a(n) is the number of directed graphs on any subset of a set of n labeled nodes, allowing self-loops (cf. A002416). - _Brent A. Yorgey_, Mar 23 2021
%H G. C. Greubel, <a href="/A135748/b135748.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) ~ 2^(n^2). - _Vaclav Kotesovec_, Nov 27 2017
%t Table[Sum[Binomial[n,k]2^k^2,{k,0,n}],{n,0,15}] (* _Harvey P. Dale_, May 30 2013 *)
%o (PARI) {a(n)=sum(k=0,n,binomial(n,k)*2^(k^2))}
%Y Cf. A002416.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 27 2007
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