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%I #28 Jan 10 2022 22:09:51
%S 1,0,16,1536,557056,731381760,3517947314176,63491024068018176,
%T 4399839304395507367936,1190389701200990489133711360,
%U 1270450770186900638201337522159616,5381052721259860098970976735257549602816,90765718885519516263620106778209295628266110976
%N Enumerates pairs consisting of a strongly connected labeled tournament and an arbitrary labeled tournament.
%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 428, see b_n.
%H Andrew Howroyd, <a href="/A054947/b054947.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) = A054946(n) * A006125(n). - _Andrew Howroyd_, Jan 10 2022
%p A054947 := proc(n)
%p option remember;
%p if n = 1 then
%p 1;
%p else
%p 2^(n*(n-1))-add(binomial(n,t)*2^((n-1)*(n-t))*procname(t),t=1..n-1) ;
%p end if;
%p end proc: # _R. J. Mathar_, May 10 2016
%t 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}];
%t Array[a, 13] (* _Jean-François Alcover_, Aug 27 2019 *)
%o (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
%Y Cf. A003030, A054946, A006125.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, May 24 2000
%E More terms from _Vladeta Jovovic_, Mar 11 2003
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