The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A094594

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A094594

Total number of edges in all connected labeled graphs on n nodes.
(history; published version)

#18 by Joerg Arndt at Tue Aug 15 03:09:01 EDT 2017

STATUS

reviewed

approved

#17 by Michel Marcus at Tue Aug 15 01:54:24 EDT 2017

STATUS

proposed

reviewed

#16 by Jon E. Schoenfield at Tue Aug 15 01:03:49 EDT 2017

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Tue Aug 15 01:03:46 EDT 2017

MAPLE

a[1]:=0: for n from 1 to 16 do a[n]:= binomial(n, 2)*2^(binomial(n, 2)-1)-sum(binomial(n, k)*2^binomial(n-k, 2)*a[k], k=1..n-1) od: seq(a[n], n=1..16); # Emeric Deutsch, Dec 18 2004

STATUS

proposed

editing

#14 by Jon E. Schoenfield at Tue Aug 15 00:53:34 EDT 2017

STATUS

editing

proposed

#13 by Jon E. Schoenfield at Tue Aug 15 00:53:31 EDT 2017

FORMULA

E.g.f.: A(x)/B(x), where A(x) is e.g.f. of A095351 and B(x) is e.g.f. of A006125. recurrence: a(n) = binomial(n, 2)*2^(binomial(n, 2) - 1) - Sum(_{k=1..n-1} binomial(n, k)*2^binomial(n-k, 2)*a(k), k=1..n-1).

MAPLE

a[1]:=0: for n from 1 to 16 do a[n]:= binomial(n, 2)*2^(binomial(n, 2)-1)-sum(binomial(n, k)*2^binomial(n-k, 2)*a[k], k=1..n-1) od: seq(a[n], n=1..16); (# _Emeric Deutsch)_

STATUS

approved

editing

#12 by Joerg Arndt at Thu Sep 05 03:19:51 EDT 2013

STATUS

proposed

approved

#11 by Geoffrey Critzer at Wed Sep 04 18:47:56 EDT 2013

STATUS

editing

proposed

#10 by Geoffrey Critzer at Wed Sep 04 18:47:45 EDT 2013

MATHEMATICA

nn=14; f[x_, y_]:=Sum[(1+y)^Binomial[n, 2]x^n/n!, {n, 0, nn}]; Drop[Range[0, nn]!CoefficientList[Series[D[Log[f[x, y]], y]/.y->1, {x, 0, nn}], x], 1] (* Geoffrey Critzer, Sep 04 2013 *)

STATUS

proposed

editing

#9 by Geoffrey Critzer at Wed Sep 04 18:24:30 EDT 2013

STATUS

editing

proposed