A202065 The number of simple labeled graphs on 2n nodes whose connected components are even length cycles.

1, 0, 3, 60, 2835, 219240, 25519725, 4169185020, 910363278825, 256123949281200, 90240816705714675, 38923077574032151500, 20174526711617730727275, 12373285262231460281715000, 8863077725980930704895768125, 7332455066541096999983523547500

Offset: 0

Author

Geoffrey Critzer, Dec 10 2011

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..225

Crossrefs

Cf. A001205, A053532, A053533.

Programs

Maple

f:= gfun:-rectoproc({(4*n^3-n)*a(n-1) + (4*n^2+2*n)*a(n) - a(n+1)=0,a(0)=1,a(1)=0},a(n),remember):
map(f, [$0..30]); # Robert Israel, Mar 02 2017

Mathematica

nn = 30; a = Log[1/(1 - x^2)^(1/4)] - x^2/4; Table[i, {i, 0, nn, 2}]! CoefficientList[Series[Exp[a], {x, 0, nn}], x][[Table[i, {i, 1, nn+1, 2}]]]
Table[((2 n)!/n!) HypergeometricPFQ[{1/4, -n}, {}, 4] (-1/4)^n, {n, 0, 15}] (* Benedict W. J. Irwin, May 24 2016 *)

Formula

E.g.f. for aerated sequence: exp(-x^2/4)/(1-x^2)^(1/4).

a(n) ~ (2*n)! * 2^(1/4)*exp(-1/4)*Gamma(3/4)/((2*n)^(3/4)*Pi). - Vaclav Kotesovec, Sep 24 2013

a(n) = ((2n)!/n!)*2F0(1/4,-n;;4)*(-1/4)^n. - Benedict W. J. Irwin, May 24 2016

(4n^3-n)a(n-1) + (4n^2+2n)a(n) - a(n+1) = 0. - Robert Israel, Mar 02 2017

Extensions

a(14) and e.g.f. corrected by Robert Israel, Mar 02 2017