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A008405 n-th derivative of x^(1/x) at x=1. 3
1, 1, -2, 3, 4, -90, 786, -5670, 34784, -136584, -824760, 33137280, -633666648, 10089623544, -145675230960, 1910939579640, -21215723677440, 136130901474240, 2280768466608576, -135531682778927808, 4380044490023909760, -119144344839822570240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = Sum_{k=0..n} Stirling1(n, k)*A003725(k). - Vladeta Jovovic, Oct 02 2003

MATHEMATICA

Function[ n, Series[ (1+x)^(1/(1+x)), {x, 0, n} ]//(Table[ SeriesCoefficient[ #, i ]*i!, {i, 0, n} ])& ][ 20 ]

a[n_] := Sum[ StirlingS1[n, k]*Sum[ (-j)^(k-j)*Binomial[k, j], {j, 0, k}], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Nov 28 2012, after Vladeta Jovovic *)

NestList[Factor[D[#1, x]] &, x^(1/x), 22] /. (x -> 1) (* Robert G. Wilson v, Feb 03 2013 *)

CROSSREFS

Sequence in context: A009496 A263281 A191422 * A037431 A262526 A171564

Adjacent sequences:  A008402 A008403 A008404 * A008406 A008407 A008408

KEYWORD

sign

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 16 02:42 EDT 2018. Contains 316252 sequences. (Running on oeis4.)