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 A340823 a(n) = exp(-1) * Sum_{k>=0} (k*(k - n))^n / k!. 1
 1, 1, 3, 5, 124, -2075, 91993, -4709903, 312334595, -25531783799, 2524083665172, -296260739274275, 40667620527027177, -6446882734412545043, 1167717545574222779643, -239452569059443831797303, 55146244227862697483251020, -14163492441645773105212592623 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = Sum_{k=0..n} binomial(n,k) * Bell(2*n-k) * (-n)^k. MATHEMATICA Table[Exp[-1] Sum[(k (k - n))^n/k!, {k, 0, Infinity}], {n, 0, 17}] Join[{1}, Table[Sum[Binomial[n, k] BellB[2 n - k] (-n)^k, {k, 0, n}], {n, 1, 17}]] CROSSREFS Cf. A000110, A020556, A020557, A290219, A334243, A340822. Sequence in context: A153137 A105526 A070743 * A245442 A215239 A161749 Adjacent sequences:  A340820 A340821 A340822 * A340824 A340825 A340826 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jan 22 2021 STATUS approved

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Last modified December 7 19:20 EST 2021. Contains 349585 sequences. (Running on oeis4.)