A054947 Enumerates pairs consisting of a strongly connected labeled tournament and an arbitrary labeled tournament.

1, 0, 16, 1536, 557056, 731381760, 3517947314176, 63491024068018176, 4399839304395507367936, 1190389701200990489133711360, 1270450770186900638201337522159616, 5381052721259860098970976735257549602816, 90765718885519516263620106778209295628266110976

Offset

1,3

References

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 428, see b_n.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

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

Formula

a(n) = A054946(n) * A006125(n). - Andrew Howroyd, Jan 10 2022

Maple

A054947 := proc(n)
    option remember;
    if n = 1 then
        1;
    else
        2^(n*(n-1))-add(binomial(n, t)*2^((n-1)*(n-t))*procname(t), t=1..n-1) ;
    end if;
end proc: # R. J. Mathar, May 10 2016

Mathematica

a[1] = 1; a[n_] := a[n] = 2^(n(n-1)) - Sum[Binomial[n, j] 2^((n-1)(n-j)) a[j], {j, 1, n-1}];
Array[a, 13] (* Jean-François Alcover, Aug 27 2019 *)

Prog

(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n]=2^(n*(n-1))-sum(j=1, n-1, binomial(n, j)*2^((n-1)*(n-j))*v[j])); v} \\ Andrew Howroyd, Sep 09 2018

Crossrefs

Cf. A003030, A054946, A006125.

Sequence in context: A178024 A221613 A266156 * A071900 A321247 A145406

Adjacent sequences: A054944 A054945 A054946 * A054948 A054949 A054950

Keyword

nonn,easy

Author

N. J. A. Sloane, May 24 2000

Extensions

More terms from Vladeta Jovovic, Mar 11 2003

Status

approved