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.

A197743 The number of connected components in all labeled directed graphs (with self loops allowed) on n nodes.

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%I A197743 #10 Nov 08 2019 09:47:35
%S A197743 0,2,20,600,70048,34265920,69135737856,563921434969088,
%T A197743 18455775305195147264,2418183926567027902291968,
%U A197743 1267698967252460350153517105152,2658483881480146168943131337243754496,22300809002478630462447974400280680553512960
%N A197743 The number of connected components in all labeled directed graphs (with self loops allowed) on n nodes.
%H A197743 Andrew Howroyd, <a href="/A197743/b197743.txt">Table of n, a(n) for n = 0..50</a>
%F A197743 E.g.f.: B(A(x)) where A(x) = log(Sum_{k=1..n} 2^(n^2)x^n/n!) and B(x)= x*exp(x).
%F A197743 a(n) = Sum_{k=1..n} k*A186236(n,k).
%t A197743 a=Sum[2^(n^2)x^n/n!, {n,0,20}]; Range[0,20]! CoefficientList[Series[a Log[a], {x,0,20}], x]
%o A197743 (PARI) seq(n)={my(g=log(sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n))); Vec(serlaplace(g*exp(g)), -(n+1))} \\ _Andrew Howroyd_, Nov 07 2019
%Y A197743 Cf. A062738, A186236.
%K A197743 nonn
%O A197743 0,2
%A A197743 _Geoffrey Critzer_, Oct 17 2011
%E A197743 Terms a(11) and beyond from _Andrew Howroyd_, Nov 07 2019