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 A052782 a(n) = (5*n+1)^(n-1). 5
 1, 1, 11, 256, 9261, 456976, 28629151, 2176782336, 194754273881, 20047612231936, 2334165173090451, 303305489096114176, 43513917611435838661, 6831675453247426400256, 1165087474585497590531111, 214481724045177216015794176, 42391158275216203514294433201 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000169, A052750, A052752, A052774, A000272, A001721. Sequence in context: A292335 A177912 A128405 * A186249 A186250 A324327 Adjacent sequences: A052779 A052780 A052781 * A052783 A052784 A052785 KEYWORD nonn,easy AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS Better description from Vladeta Jovovic, Sep 02 2003 STATUS approved

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Last modified September 18 23:03 EDT 2024. Contains 376002 sequences. (Running on oeis4.)