A052519 Number of pairs of cycles of cardinality at least 3.

0, 0, 0, 0, 0, 0, 80, 840, 7896, 76608, 793152, 8838720, 106096320, 1368956160, 18928615680, 279530334720, 4394135692800, 73295141068800, 1293442388582400, 24082259707699200, 471874122729676800

Offset

0,7

Links

G. C. Greubel, Table of n, a(n) for n = 0..448

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 85

Formula

E.g.f.: log(1-x)^2 + x*(2+x)*log(1-x) + x^2 + x^3 + x^4/4.

(n-1)*a(n+2) + (3+n-2*n^2)*a(n+1) - n*(2+n-n^2)*a(n) = 0, with a(0) = .. = a(5) = 0, a(6) = 80.

Maple

Pairs spec := [S, {B=Cycle(Z, 3 <= card), S=Prod(B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

With[{m = 25}, CoefficientList[Series[Log[1-x]^2 +x*(2+x)*Log[1-x] +x^2 + x^3 +x^4/4, {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 13 2019 *)

Prog

(PARI) my(x='x+O('x^25)); concat(vector(6), Vec(serlaplace( log(1-x)^2 + x*(2+x)*log(1-x) + x^2 + x^3 + x^4/4 ))) \\ G. C. Greubel, May 13 2019
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Log(1-x)^2 + x*(2+x)*Log(1-x) + x^2 + x^3 + x^4/4 )); [0, 0, 0, 0, 0, 0] cat [Factorial(n+5)*b[n]: n in [1..m-6]]; // G. C. Greubel, May 13 2019
(Sage) m = 25; T = taylor(log(1-x)^2 + x*(2+x)*log(1-x) + x^2 + x^3 + x^4/4, x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 13 2019

Crossrefs

Sequence in context: A062911 A024392 A200550 * A246545 A198400 A182680

Adjacent sequences: A052516 A052517 A052518 * A052520 A052521 A052522

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved