A054949 - OEIS

%I #18 Aug 27 2019 10:53:12

%S 1,1,19,1612,565276,734799976,3523103676184,63519230066936512,

%T 4400411105398828102336,1190433708177460323642937216,

%U 1270463865199882936737403300783744,5381067966904826663696685903449569172992,90765788839502187660342772995967835888789034496

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

%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) = (A054948(n) + A054947(n))/2. - _Andrew Howroyd_, Sep 10 2018

%t A054947[1] = 1; A054947[n_] := A054947[n] = 2^(n(n - 1)) - Sum[Binomial[n, j] 2^((n - 1)(n - j)) A054947[j], {j, 1, n - 1}];

%t A054948[0] = 1; A054948[n_] := A054948[n] = Module[{A}, A = 1 + Sum[ A054948[k]*x^k/k!, {k, 1, n - 1}]; n!*SeriesCoefficient[Sum[2^(k^2 - k)*x^k/k!/(A /. x -> 2^k*x) , {k, 0, n}], {x, 0, n}]];

%t a[n_] := (A054948[n] + A054947[n])/2;

%t Array[a, 13] (* _Jean-François Alcover_, Aug 27 2019 *)

%Y Cf. A054947, A054948, A054950.

%K nonn,easy

%O 1,3

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

%E More terms from _Vladeta Jovovic_, Mar 11 2003