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A253276 Number of undirected labeled graphs on 2n nodes with exactly n cycle graphs as connected components. 2
1, 1, 7, 120, 3157, 109935, 4754200, 245722477, 14779601837, 1014260971581, 78214593177825, 6696084566881710, 630196627700087272, 64671387743952373150, 7186999700934499032405, 859879811676654352591875, 110201017079975901129209565, 15061748014412378814910531365 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)