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A349852
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Expansion of Sum_{k>=0} k * x^k/(1 + k * x).
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4
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0, 1, 1, 0, 2, 1, -5, 20, -28, -47, 525, -2056, 3902, 9633, -129033, 664364, -1837904, -2388687, 67004697, -478198544, 1994889946, -1669470783, -56929813933, 615188040196, -3794477505572, 12028579019537, 50780206473221, -1172949397924184, 10766410530764118
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = -Sum_{k=0..n} (-k)^(n-k+1).
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MATHEMATICA
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a[n_] := -Sum[(-k)^(n - k + 1), {k, 0, n}]; Array[a, 29, 0] (* Amiram Eldar, Dec 02 2021 *)
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PROG
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(PARI) a(n, s=1, t=1) = sum(k=0, n, (-k^t)^(n-k)*k^s);
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k*x^k/(1+k*x))))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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