cp's OEIS Frontend

A173313 Partial sums of A000273.

%I A173313 #12 Jul 05 2024 16:12:09
%S A173313 1,2,5,21,239,9847,1550791,883584231,1794242777079,13029751067176631,
%T A173313 341273461704039756983,32523250658517590150954423,
%U A173313 11366777954076059092024044958647,14669097059490883945096188099361179575,70315671284332059012269451652168003452397495
%N A173313 Partial sums of A000273.
%C A173313 Partial sums of number of directed graphs (or digraphs) with n nodes. The subsequence of primes in this partial sum begins 2, 5, 239, then no more through a(20).
%C A173313 a(n) is the number of isolated points over all directed graphs with (n + 1) nodes. - _Geoffrey Critzer_, Oct 08 2012
%H A173313 Chai Wah Wu, <a href="/A173313/b173313.txt">Table of n, a(n) for n = 0..60</a>
%F A173313 a(n) = Sum_{i=0..n} A000273(i).
%F A173313 O.g.f.: A(x)/(1-x) where A(x) is the o.g.f. for A000273. - _Geoffrey Critzer_, Oct 08 2012
%e A173313 a(12) = 1 + 1 + 3 + 16 + 218 + 9608 + 1540944 + 882033440 + 1793359192848 + 13027956824399552 + 341260431952972580352 + 32522909385055886111197440 + 11366745430825400574433894004224.
%p A173313 b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(p[j]-1+add(
%p A173313       igcd(p[k], p[j]), k=1..j-1)*2, j=1..nops(p)))([l[], 1$n])),
%p A173313       add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
%p A173313     end:
%p A173313 a:= proc(n) option remember; b(n$2, [])+`if`(n=0, 0, a(n-1)) end:
%p A173313 seq(a(n), n=0..16);  # _Alois P. Heinz_, Sep 04 2019
%t A173313 nn=20;d=Sum[NumberOfDirectedGraphs[n]x^n,{n,0,nn}];CoefficientList[Series[d/(1-x),{x,0,nn}],x]
%Y A173313 Cf. A000273.
%K A173313 nonn
%O A173313 0,2
%A A173313 _Jonathan Vos Post_, Feb 16 2010