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

Author

N. J. A. Sloane, May 24 2000

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A003030, A054946, A006125.

Programs

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 *)

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

Formula

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

Extensions

More terms from Vladeta Jovovic, Mar 11 2003