OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..313
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 739
J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014.
FORMULA
E.g.f.: exp(-1/5*LambertW(-5*x)).
From Peter Bala, Dec 19 2013: (Start)
The e.g.f. A(x) = 1 + x + 11*x^2/2! + 256*x^3/3! + 9261*x^4/4! + ... satisfies:
1) A(x*exp(-5*x)) = exp(x) = 1/A(-x*exp(5*x));
2) A^5(x) = 1/x*series reversion(x*exp(-5*x));
3) A(x^5) = 1/x*series reversion(x*exp(-x^5));
4) A(x) = exp(x*A(x)^5);
5) A(x) = 1/A(-x*A(x)^10). (End)
E.g.f.: (-LambertW(-5*x)/(5*x))^(1/5). - Vaclav Kotesovec, Dec 07 2014
Related to A001721 by Sum_{n >= 1} a(n)*x^n/n! = series reversion( 1/(1 + x)^5*log(1 + x) ) = series reversion(x - 11*x^2/2! + 107*x^3/3! - 1066*x^4/4! + ...). Cf. A000272, A052750. - Peter Bala, Jun 15 2016
MAPLE
spec := [S, {S=Set(B), B=Prod(Z, S, S, S, S, S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[Exp[-LambertW[-5*x]/5], {x, 0, nmax}], x]*Range[0, nmax]!] (* or *) Table[(5*n+1)^(n-1), {n, 0, 50}] (* G. C. Greubel, Nov 16 2017 *)
PROG
(PARI) for(n=0, 50, print1((5*n+1)^(n-1), ", ")) \\ G. C. Greubel, Nov 16 2017
(PARI) x='x+O('x^50); Vec(serlaplace(exp(-lambertw(-5*x)/5))) \\ G. C. Greubel, Nov 16 2017
(Magma) [(5*n+1)^(n-1): n in [0..50]]; // G. C. Greubel, Nov 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
Better description from Vladeta Jovovic, Sep 02 2003
STATUS
approved