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

%I A253276 #14 Feb 26 2017 10:50:56
%S A253276 1,1,7,120,3157,109935,4754200,245722477,14779601837,1014260971581,
%T A253276 78214593177825,6696084566881710,630196627700087272,
%U A253276 64671387743952373150,7186999700934499032405,859879811676654352591875,110201017079975901129209565,15061748014412378814910531365
%N A253276 Number of undirected labeled graphs on 2n nodes with exactly n cycle graphs as connected components.
%H A253276 Alois P. Heinz, <a href="/A253276/b253276.txt">Table of n, a(n) for n = 0..200</a>
%F A253276 a(n) = A215771(2n,n).
%F A253276 a(n) ~ c * d^n * (n-1)!, where d = 8.52944416851968239902405793921886268..., c = 0.1101477123991489575407024889... . - _Vaclav Kotesovec_, May 01 2015
%p A253276 b:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1,
%p A253276       add(binomial(n-1, i)*b(n-1-i, k-1)*ceil(i!/2), i=0..n-k)))
%p A253276     end:
%p A253276 a:= n-> b(2*n, n):
%p A253276 seq(a(n), n=0..20);
%t A253276 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 *)
%Y A253276 Cf. A215771.
%K A253276 nonn
%O A253276 0,3
%A A253276 _Alois P. Heinz_, May 01 2015