A213236 a(n) = (-n)^(n-1).

1, -2, 9, -64, 625, -7776, 117649, -2097152, 43046721, -1000000000, 25937424601, -743008370688, 23298085122481, -793714773254144, 29192926025390625, -1152921504606846976, 48661191875666868481, -2185911559738696531968, 104127350297911241532841

Offset: 1

Author

Michael Somos, Jun 07 2012

Keywords

• sign

Examples

			x - 2*x^2 + 9*x^3 - 64*x^4 + 625*x^5 - 7776*x^6 + 117649*x^7 + ...
		

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function
• Wikipedia, Lambert W function

Crossrefs

Cf. A000027, A000169.

Programs

Magma

[(-n)^(n-1) : n in [1..20]]; // Wesley Ivan Hurt, Jan 17 2017

Maple

a := proc(n); `if`( n<0, 0, n! * coeff( taylor( LambertW(x), x=0, n+1 ), x, n)); end;

Mathematica

a[ n_] := If[ n < 0, 0, n! SeriesCoefficient[ ProductLog @ z, {z, 0, n}]]
Table[(-n)^(n-1),{n,30}] (* Harvey P. Dale, Apr 29 2013 *)

PARI

{a(n) = if( n<1, 0, (-n) ^ (n-1))}

PARI

{a(n) = if( n<1, 0, n! * polcoeff( serreverse( x * exp(x + x * O(x^n))), n))}

PARI

{a(n) = local(A); if( n<1, 0, A = O(x); for( k=1, n, A = x / exp(A)); n! * polcoeff( A, n))}

Formula

E.g.f.: LambertW(x).

E.g.f. is the functional inverse of x * exp(x) which is the e.g.f. of A000027.

E.g.f. A(x) satisfies A(x) = x / exp(A(x)).

a(n) = -(-1)^n * A000169(n).