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A151884 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. 4
1, 4, 14, 56, 304, 1904, 14048, 112384, 1051776, 10662912, 120920832, 1451049984, 19342651392, 272576268288, 4175822315520, 66813157048320, 1156746459709440, 20900477925457920, 403511454289428480, 8070229085788569600, 171907712809736601600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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)

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::odd, [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_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-Fran├žois Alcover, Mar 13 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A000254, A151881, A151882, A151883, A081358, A092691.

Sequence in context: A073155 A006212 A126701 * A002735 A026652 A269134

Adjacent sequences:  A151881 A151882 A151883 * A151885 A151886 A151887

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 22 2009

STATUS

approved

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Last modified November 18 13:22 EST 2018. Contains 317306 sequences. (Running on oeis4.)