cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A135748 a(n) = Sum_{k=0..n} binomial(n,k)*2^(k^2).

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