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
(SageMath) 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
KEYWORD
easy,nonn
AUTHOR
INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000
STATUS
approved