A355376 a(n) = Sum_{k=0..n} k! * (-k)^(n-k) * Stirling2(n,k).
1, 1, 1, -5, -29, 271, 3091, -61025, -744029, 34875871, 211095331, -37415273345, 300267009571, 61080483836191, -2133136977892829, -119576844586022465, 11752559492568148771, 94348367247493654111, -68793303669649907424989, 2764486881197709482575615
Offset: 0
Keywords
Programs
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Mathematica
a[n_] := Sum[k! * (-k)^(n - k) * StirlingS2[n, k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0] (* Amiram Eldar, Jun 30 2022 *) -
PARI
a(n) = sum(k=0, n, k!*(-k)^(n-k)*stirling(n, k, 2));
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (1-exp(-k*x))^k/k^k)))
Formula
E.g.f.: Sum_{k>=0} (1 - exp(-k * x))^k / k^k.