A141151 L.g.f.: A(x) = log( Sum_{n>=0} n^n*x^n ) = Sum_{n>=1} a(n)*x^n/n.

1, 7, 70, 899, 14001, 255532, 5342541, 125876003, 3300437302, 95338188007, 3009043615073, 103043811158864, 3805827820399125, 150819894172935183, 6383815674758486310, 287459477551898694403, 13721584934214631377921

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..385

Formula

a(n) ~ n^(n+1). - Vaclav Kotesovec, May 30 2019

Example

L.g.f.: A(x) = x + 7*x^2/2 + 70*x^3/3 + 899*x^4/4 + 14001*x^5/5 + ...
exp(A(x)) = 1 + x + 4*x^2 + 27*x^3 + 256*x^4 + 3125*x^5 + 46656*x^6 + ...

Mathematica

With[{m=20}, Drop[CoefficientList[Series[Log[Sum[If[n==0, 1, n^n*x^n], {n, 0, m+2}]], {x, 0, m}], x], 1]*Range[1, m]] (* G. C. Greubel, May 30 2019 *)

Prog

(PARI) {a(n)=polcoeff(x*deriv(log(Ser(concat(1, vector(n+1, k, k^k))))), n)}
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Log( (&+[n^n*x^n: n in [0..m+2]]) ) )); [n*b[n]: n in [1..m-1]]; // G. C. Greubel, May 30 2019
(Sage) m = 20; T = taylor(log( sum(n^n*x^n for n in (0..m+2)) ), x, 0, m); [n*T.coefficient(x, n) for n in (1..m)] # G. C. Greubel, May 30 2019

Crossrefs

Cf. A141152, A306628.

Sequence in context: A226805 A113343 A124566 * A001669 A051604 A346668

Adjacent sequences: A141148 A141149 A141150 * A141152 A141153 A141154

Keyword

nonn

Author

Paul D. Hanna, Jun 11 2008

Status

approved