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A052518 Number of pairs of cycles of cardinality at least 2. 2
0, 0, 0, 0, 6, 40, 260, 1848, 14616, 128448, 1246752, 13273920, 153996480, 1935048960, 26193473280, 380120670720, 5888620684800, 97007636275200, 1693590745190400, 31237853849395200, 607035345406156800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..445

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 84

FORMULA

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

n*a(n+2) + (1-n-2*n^2)*a(n+1) - n*(1-n^2)*a(n) = 0, with a(0) = ... = a(3) = 0, a(4) = 3!.

a(n) = 2*(n-2)!*((n-1)*(Psi(n) + gamma) - n), n>2. - Vladeta Jovovic, Sep 21 2003

MAPLE

Pairs spec := [S, {B=Cycle(Z, 2 <= 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 +2*x*Log[1-x] +x^2, {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 13 2019 *)

PROG

(PARI) a(n) = if (n <= 2, 0, round(2*(n-2)!*((n-1)*(psi(n)+Euler)-n))); \\ Michel Marcus, Jul 08 2015

(PARI) my(x='x+O('x^25)); concat(vector(4), Vec(serlaplace( log(1-x)^2 + 2*x*log(1-x) + x^2 ))) \\ G. C. Greubel, May 13 2019

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Log(1-x)^2 + 2*x*Log(1-x) + x^2 )); [0, 0, 0, 0] cat [Factorial(n+3)*b[n]: n in [1..m-4]]; // G. C. Greubel, May 13 2019

(Sage) m = 25; T = taylor(log(1-x)^2 + 2*x*log(1-x) + x^2, x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 13 2019

CROSSREFS

Cf. A000254, A000276.

Sequence in context: A254945 A026077 A065113 * A135032 A122074 A289208

Adjacent sequences:  A052515 A052516 A052517 * A052519 A052520 A052521

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified July 22 08:31 EDT 2019. Contains 325216 sequences. (Running on oeis4.)