A151883 - OEIS

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.

%I #11 Mar 13 2017 04:22:05

%S 0,1,3,24,120,840,5880,54600,491400,5276880,58045680,749770560,

%T 9747017280,142685262720,2140278940800,35879056012800,609943952217600,

%U 11334678568012800,215358892792243200,4453151976335462400,93516191503044710400,2108447155238693068800

%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 even} (j_i)^2.

%H N. J. A. Sloane and Alois P. Heinz, <a href="/A151883/b151883.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::even, [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_] := 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_ *)

%Y Cf. A000254, A151881, A151882, A151884, A092691, A081358.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jul 22 2009