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 A292866 a(n) = n! * [x^n] exp(n*(1 - exp(x))). 10
 1, -1, 2, -3, -20, 370, -4074, 34293, -138312, -2932533, 106271090, -2192834490, 32208497124, -206343936097, -7657279887698, 412496622532785, -12455477719752976, 260294034150380430, -2256541295745391542, -122593550603339550843, 8728842979656718306780 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..415 FORMULA a(n) = exp(n) * Sum_{k>=0} (-n)^k*k^n/k!. - Ilya Gutkovskiy, Jul 13 2019 a(n) = Sum_{k=0..n} (-n)^k * Stirling2(n,k). - Seiichi Manyama, Jul 28 2019 a(n) = BellPolynomial(n, -n). - Peter Luschny, Dec 23 2021 MAPLE b:= proc(n, k) option remember; `if`(n=0, 1,       -(1+add(binomial(n-1, j-1)*b(n-j, k), j=1..n-1))*k)     end: a:= n-> b(n\$2): seq(a(n), n=0..30);  # Alois P. Heinz, Sep 25 2017 MATHEMATICA Table[n!*SeriesCoefficient[E^(n*(1 - E^x)), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 25 2017 *) a[n_] := BellB[n, -n]; Table[a[n], {n, 0, 20}] (* Peter Luschny, Dec 23 2021 *) PROG (Ruby) def ncr(n, r)   return 1 if r == 0   (n - r + 1..n).inject(:*) / (1..r).inject(:*) end def A(k, n)   ary = [1]   (1..n).each{|i| ary << k * (0..i - 1).inject(0){|s, j| s + ncr(i - 1, j) * ary[j]}}   ary end def A292866(n)   (0..n).map{|i| A(-i, i)[-1]} end p A292866(20) (PARI) {a(n) = sum(k=0, n, (-n)^k*stirling(n, k, 2))} \\ Seiichi Manyama, Jul 28 2019 CROSSREFS Main diagonal of A292861. Cf. A242817. Sequence in context: A006246 A349600 A110372 * A132421 A132500 A129411 Adjacent sequences:  A292863 A292864 A292865 * A292867 A292868 A292869 KEYWORD sign AUTHOR Seiichi Manyama, Sep 25 2017 STATUS approved

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Last modified July 3 22:14 EDT 2022. Contains 355058 sequences. (Running on oeis4.)