A253276 Number of undirected labeled graphs on 2n nodes with exactly n cycle graphs as connected components.

1, 1, 7, 120, 3157, 109935, 4754200, 245722477, 14779601837, 1014260971581, 78214593177825, 6696084566881710, 630196627700087272, 64671387743952373150, 7186999700934499032405, 859879811676654352591875, 110201017079975901129209565, 15061748014412378814910531365

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = A215771(2n,n).

a(n) ~ c * d^n * (n-1)!, where d = 8.52944416851968239902405793921886268..., c = 0.1101477123991489575407024889... . - Vaclav Kotesovec, May 01 2015

Maple

b:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1,
      add(binomial(n-1, i)*b(n-1-i, k-1)*ceil(i!/2), i=0..n-k)))
    end:
a:= n-> b(2*n, n):
seq(a(n), n=0..20);

Mathematica

b[n_, k_] := b[n, k] = If[k<0 || k>n, 0, If[n==0, 1, Sum[Binomial[n-1, i]*b[n-1-i, k-1]*Ceiling[i!/2], {i, 0, n-k}]]]; a[n_] := b[2 n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 26 2017, translated from Maple *)

Crossrefs

Cf. A215771.

Sequence in context: A302718 A007751 A193785 * A156955 A196796 A196583

Adjacent sequences: A253273 A253274 A253275 * A253277 A253278 A253279

Keyword

nonn

Author

Alois P. Heinz, May 01 2015

Status

approved