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 A337043 a(0) = 1; thereafter a(n) = exp(-1/n) * Sum_{k>=0} (n*k - 1)^n / (n^k * k!). 5
 1, 0, 2, 9, 112, 1875, 43416, 1310946, 49778688, 2313362673, 128894500000, 8469572721533, 647341071298560, 56871349337125648, 5684260661585401728, 640631299771142578125, 80788871646072851660800, 11323828537291632967145015, 1753760620207362607774290432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = [x^n] (1/(1 + x)) * Sum_{k>=0} (x/(1 + x))^k / Product_{j=1..k} (1 - n*j*x/(1 + x)). a(n) = n! * [x^n] exp((exp(n*x) - 1) / n - x), for n > 0. a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * n^k * BellPolynomial_k(1/n), for n > 0. MATHEMATICA Table[SeriesCoefficient[1/(1 + x) Sum[(x/(1 + x))^k/Product[(1 - n j x/(1 + x)), {j, 1, k}], {k, 0, n}], {x, 0, n}], {n, 0, 18}] Join[{1}, Table[n! SeriesCoefficient[Exp[(Exp[n x] - 1)/n - x], {x, 0, n}], {n, 1, 18}]] Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k, 1/n], {k, 0, n}], {n, 1, 18}]] CROSSREFS Cf. A000296, A301419, A330605, A334162, A337038, A337039, A337040, A337041, A337042. Sequence in context: A339015 A305005 A326267 * A008269 A039718 A307249 Adjacent sequences:  A337040 A337041 A337042 * A337044 A337045 A337046 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Aug 12 2020 STATUS approved

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)