A151883 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 even} (j_i)^2.
0, 1, 3, 24, 120, 840, 5880, 54600, 491400, 5276880, 58045680, 749770560, 9747017280, 142685262720, 2140278940800, 35879056012800, 609943952217600, 11334678568012800, 215358892792243200, 4453151976335462400, 93516191503044710400, 2108447155238693068800
Offset: 1
Keywords
Links
- N. J. A. Sloane and Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 30 terms from N. J. A. Sloane)
Programs
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Maple
with(combinat): b:= proc(n, i) option remember; `if`(n=0, [1,0], `if`(i<1, 0, add(multinomial(n,n-i*j,i$j)/j!*(i-1)!^j*(p-> p+ `if`(i::even, [0, p[1]*j^2], 0))(b(n-i*j, i-1)), j=0..n/i))) end: a:= n-> b(n$2)[2]: seq(a(n), n=1..30); # Alois P. Heinz, Oct 21 2015 -
Mathematica
multinomial[n_, k_] := 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[EvenQ[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 *)