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 A331582 a(n) = n! * [x^n] exp(n - exp(x) * (exp(n*x) - 1) / (exp(x) - 1)). 1
 1, -1, 4, 0, -1654, 102750, -4079389, -178722208, 83191059372, -14561829897345, 1115121827539325, 403631463559529040, -251989999508801085674, 76158421344845152140737, -3994730250899559184766830, -13162858116922635098226480000, 10823217968258750568539067678392 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..200 FORMULA a(n) = n! * [x^n] exp(n - exp(x) - exp(2*x) - exp(3*x) - ... - exp(n*x)). MATHEMATICA Table[n! SeriesCoefficient[Exp[n - Exp[x] (Exp[n x] - 1)/(Exp[x] - 1)], {x, 0, n}], {n, 0, 16}] b[n_, k_] := b[n, k] = If[n == 0, 1, -Sum[Binomial[n - 1, j - 1] Sum[i^j, {i, 1, k}] b[n - j, k], {j, 1, n}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 16}] CROSSREFS Cf. A103438, A319508, A319509, A320288. Sequence in context: A130105 A013463 A013464 * A306819 A327113 A051390 Adjacent sequences:  A331579 A331580 A331581 * A331583 A331584 A331585 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jan 21 2020 STATUS approved

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Last modified September 26 11:29 EDT 2020. Contains 337367 sequences. (Running on oeis4.)