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%I #10 Mar 13 2017 09:04:22
%S 1,4,14,56,304,1904,14048,112384,1051776,10662912,120920832,
%T 1451049984,19342651392,272576268288,4175822315520,66813157048320,
%U 1156746459709440,20900477925457920,403511454289428480,8070229085788569600,171907712809736601600
%N Let g be a permutation of [1..n] having say j_i cycles of length i, with Sum_i i*j_i = n; sequence gives Sum_g Sum_{i odd} (j_i)^2.
%H N. J. A. Sloane and Alois P. Heinz, <a href="/A151884/b151884.txt">Table of n, a(n) for n = 1..450</a> (first 30 terms from N. J. A. Sloane)
%p with(combinat):
%p b:= proc(n, i) option remember; `if`(n=0, [1,0], `if`(i<1, 0,
%p add(multinomial(n,n-i*j,i$j)/j!*(i-1)!^j*(p-> p+
%p `if`(i::odd, [0, p[1]*j^2], 0))(b(n-i*j, i-1)), j=0..n/i)))
%p end:
%p a:= n-> b(n$2)[2]:
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Oct 21 2015
%t multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n==0, {1, 0}, If[i<1, {0, 0}, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*(i-1)!^j*Function[p, p+If[OddQ[i], {0, p[[1]]*j^2}, {0, 0}]][b[n-i*j, i-1]], {j, 0, n/i}]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Mar 13 2017, after _Alois P. Heinz_ *)
%Y Cf. A000254, A151881, A151882, A151883, A081358, A092691.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jul 22 2009
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