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

0,3

Links

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

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

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 *)

Crossrefs

Cf. A001205, A053532, A053533.

Sequence in context: A361536 A081854 A085990 * A036770 A201699 A006821

Adjacent sequences: A202062 A202063 A202064 * A202066 A202067 A202068

Keyword

nonn

Author

Geoffrey Critzer, Dec 10 2011

Extensions

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

Status

approved