A173313 Partial sums of A000273.

1, 2, 5, 21, 239, 9847, 1550791, 883584231, 1794242777079, 13029751067176631, 341273461704039756983, 32523250658517590150954423, 11366777954076059092024044958647, 14669097059490883945096188099361179575, 70315671284332059012269451652168003452397495

Offset

0,2

Comments

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).

a(n) is the number of isolated points over all directed graphs with (n + 1) nodes. - Geoffrey Critzer, Oct 08 2012

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = Sum_{i=0..n} A000273(i).

O.g.f.: A(x)/(1-x) where A(x) is the o.g.f. for A000273. - Geoffrey Critzer, Oct 08 2012

Example

a(12) = 1 + 1 + 3 + 16 + 218 + 9608 + 1540944 + 882033440 + 1793359192848 + 13027956824399552 + 341260431952972580352 + 32522909385055886111197440 + 11366745430825400574433894004224.

Maple

b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(p[j]-1+add(
      igcd(p[k], p[j]), k=1..j-1)*2, j=1..nops(p)))([l[], 1$n])),
      add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
    end:
a:= proc(n) option remember; b(n$2, [])+`if`(n=0, 0, a(n-1)) end:
seq(a(n), n=0..16);  # Alois P. Heinz, Sep 04 2019

Mathematica

nn=20; d=Sum[NumberOfDirectedGraphs[n]x^n, {n, 0, nn}]; CoefficientList[Series[d/(1-x), {x, 0, nn}], x]

Crossrefs

Cf. A000273.

Sequence in context: A357871 A216756 A007570 * A210575 A174143 A298762

Adjacent sequences: A173310 A173311 A173312 * A173314 A173315 A173316

Keyword

nonn

Author

Jonathan Vos Post, Feb 16 2010

Status

approved