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 A213236 a(n) = (-n)^(n-1). 0
 1, -2, 9, -64, 625, -7776, 117649, -2097152, 43046721, -1000000000, 25937424601, -743008370688, 23298085122481, -793714773254144, 29192926025390625, -1152921504606846976, 48661191875666868481, -2185911559738696531968, 104127350297911241532841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Eric Weisstein's World of Mathematics, Lambert W-Function Wikipedia, Lambert W function 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). EXAMPLE x - 2*x^2 + 9*x^3 - 64*x^4 + 625*x^5 - 7776*x^6 + 117649*x^7 + ... 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 *) PROG (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))} (MAGMA) [(-n)^(n-1) : n in [1..20]]; // Wesley Ivan Hurt, Jan 17 2017 CROSSREFS Cf. A000027, A000169. Sequence in context: A325208 A055860 A152917 * A000169 A112319 A232552 Adjacent sequences:  A213233 A213234 A213235 * A213237 A213238 A213239 KEYWORD sign AUTHOR Michael Somos, Jun 07 2012 STATUS approved

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Last modified October 23 22:28 EDT 2019. Contains 328373 sequences. (Running on oeis4.)