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%I #7 Dec 12 2020 04:44:41
%S 1,1,7,42,931,6078,560124,3451290,504673027,10212362573,1083069266634,
%T 17595339114554,13211434169884204,109469680507411214,
%U 36642712015230282784,3131089417758323092388,735014776353108421594259,19549131844625243949179686
%N Number of set partitions of [n^2] that are invariant under a permutation consisting of n n-cycles.
%H Alois P. Heinz, <a href="/A293850/b293850.txt">Table of n, a(n) for n = 0..281</a>
%F a(n) = A162663(n,n).
%p b:= proc(n, k) option remember; `if`(n=0, 1, add(binomial(n-1, j-1)
%p *add(d^(j-1), d=numtheory[divisors](k))*b(n-j, k), j=1..n))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..18);
%t b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[Binomial[n - 1, j - 1] Sum[d^(j - 1), {d, Divisors[k]}] b[n - j, k], {j, 1, n}]];
%t a[n_] := b[n, n];
%t a /@ Range[0, 18] (* _Jean-François Alcover_, Dec 12 2020, after _Alois P. Heinz_ *)
%Y Cf. A162663.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 17 2017
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