A152917 A000169 prefixed by an initial 0.

0, 1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000, 25937424601, 743008370688, 23298085122481, 793714773254144, 29192926025390625, 1152921504606846976, 48661191875666868481, 2185911559738696531968, 104127350297911241532841

Offset

0,3

Comments

A variant of A000169, which is the main entry for this sequence. - N. J. A. Sloane, Dec 19 2008

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = 0 if n = 0, otherwise a(n) = n^(n-1).

E.g.f.: A(x)=x*G(0) ; G(k)= 1 + x*(2*k+2)^(2*k)/((2*k+1)^(2*k) - x*(2*k+1)^(2*k)*(2*k+3)^(2*k+1)/(x*(2*k+3)^(2*k+1) + (2*k+2)^(2*k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Dec 30 2011

E.g.f.: -LambertW(-x). - Alois P. Heinz, Feb 26 2020

Example

a(10) = 10^9 = 1000000000.

Mathematica

Join[{0}, Table[n^(n-1), {n, 20}]] (* Harvey P. Dale, Jan 28 2017 *)

Crossrefs

Cf. A000169.

Sequence in context: A325207 A325208 A055860 * A213236 A000169 A112319

Adjacent sequences: A152914 A152915 A152916 * A152918 A152919 A152920

Keyword

nonn

Author

ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 15 2008

Status

approved