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A052519 Number of pairs of cycles of cardinality at least 3. 1
0, 0, 0, 0, 0, 0, 80, 840, 7896, 76608, 793152, 8838720, 106096320, 1368956160, 18928615680, 279530334720, 4394135692800, 73295141068800, 1293442388582400, 24082259707699200, 471874122729676800 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

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

STATUS

approved

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Last modified May 22 06:32 EDT 2019. Contains 323478 sequences. (Running on oeis4.)