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 A334258 a(n) = (-1)^n * exp(n) * Sum_{k>=1} (-1)^k * n^(k-1) * k^n / k!. 0
 1, 1, 1, -5, -74, -679, -4899, -17289, 325837, 10627109, 199348590, 2684041427, 15872610469, -546948563407, -27499774835519, -778467357484561, -15311413773551790, -125363405319188419, 6452292137017871097, 436442148982835915339, 16494863323310244977581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Table of n, a(n) for n=1..21. Eric Weisstein's World of Mathematics, Bell Polynomial FORMULA E.g.f.: series reversion of -log(1 - x) * exp(-x). a(n) = (n - 1)! * [x^n] exp(n*(1 - exp(-x))). a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling2(n,k) * n^(k-1). a(n) = (-1)^n * BellPolynomial_n(-n) / n. MATHEMATICA nmax = 21; CoefficientList[InverseSeries[Series[-Log[1 - x] Exp[-x], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest Table[Sum[(-1)^(n - k) StirlingS2[n, k] n^(k - 1), {k, 1, n}], {n, 1, 21}] Table[(-1)^n BellB[n, -n]/n, {n, 1, 21}] PROG (PARI) a(n) = sum(k=1, n, (-1)^(n-k) * stirling(n, k, 2) * n^(k-1)); \\ Michel Marcus, Apr 20 2020 CROSSREFS Cf. A002741, A052888, A292866. Sequence in context: A131958 A051156 A092826 * A322446 A065894 A233013 Adjacent sequences: A334255 A334256 A334257 * A334259 A334260 A334261 KEYWORD sign AUTHOR Ilya Gutkovskiy, Apr 20 2020 STATUS approved

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Last modified May 30 12:50 EDT 2023. Contains 363050 sequences. (Running on oeis4.)