A054953 - OEIS

%I #22 Jan 15 2022 12:29:42

%S 1,1,5,83,5048,1047013,705422455,1580348377261,12139024826336632,

%T 328160951350054991463,31831080872414173375174213,

%U 11234274997368911879051177335450,14576252633139821208116086572516525403,70075713785837731364265242597960381223077163

%N Number of unlabeled semi-strong digraphs on n nodes with an odd number of pairwise different components.

%H Andrew Howroyd, <a href="/A054953/b054953.txt">Table of n, a(n) for n = 1..50</a>

%H V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.

%F a(n) = (A054952(n) + A054951(n))/2. - _Andrew Howroyd_, Sep 10 2018

%t m = 15;

%t A035512 = Cases[Import["https://oeis.org/A035512/b035512.txt", "Table"], {_, _}][[All, 2]];

%t gf = -Product[(1 - x^n)^A035512[[n + 1]], {n, 1, m}] + Product[(1 + x^n)^A035512[[n + 1]], {n, 1, m}];

%t CoefficientList[gf + O[x]^m , x]/2 // Rest (* _Jean-François Alcover_, Aug 26 2019, after _Andrew Howroyd_ *)

%Y Cf. A054951, A054952, A054954.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, May 24 2000

%E More terms from _Vladeta Jovovic_, Mar 11 2003

%E a(12)-a(14) from _Andrew Howroyd_, Sep 10 2018