A054949 Number of labeled semi-strong digraphs on n nodes with an odd number of components.

1, 1, 19, 1612, 565276, 734799976, 3523103676184, 63519230066936512, 4400411105398828102336, 1190433708177460323642937216, 1270463865199882936737403300783744, 5381067966904826663696685903449569172992, 90765788839502187660342772995967835888789034496

Offset

1,3

Links

Table of n, a(n) for n=1..13.

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Formula

a(n) = (A054948(n) + A054947(n))/2. - Andrew Howroyd, Sep 10 2018

Mathematica

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}];
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}]];
a[n_] := (A054948[n] + A054947[n])/2;
Array[a, 13] (* Jean-François Alcover, Aug 27 2019 *)

Crossrefs

Cf. A054947, A054948, A054950.

Sequence in context: A002115 A223498 A352465 * A375219 A242564 A068748

Adjacent sequences: A054946 A054947 A054948 * A054950 A054951 A054952

Keyword

nonn,easy

Author

N. J. A. Sloane, May 24 2000

Extensions

More terms from Vladeta Jovovic, Mar 11 2003

Status

approved