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URL: https://oeis.org/A308024

⇱ A308024 - OEIS

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A308024
G.f. A(x) satisfies: A(x) = x * (1 + (1/(1 + x)) * (A(x/(1 + x)) + A(x^2/(1 + x)^2) + A(x^3/(1 + x)^3) + ...)).
1
1, 1, 0, -2, 4, 0, -24, 68, 20, -936, 3800, -2172, -64120, 417752, -959852, -5464092, 68816400, -328509112, 8361828, 13473157664, -119068537700, 448312242012, 1868795480588, -43889516937276, 348963546501928, -1006637409183472, -12316833304447344, 217304253286437480
OFFSET
1,4
FORMULA
a(1) = 1; a(n+1) = Sum_{k=1..n} (-1)^(n-k)*binomial(n,k) * Sum_{d|k} a(d).
MATHEMATICA
terms = 28; A[_] = 0; Do[A[x_] = x (1 + 1/(1 + x) Sum[A[x^k/(1 + x)^k], {k, 1, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
a[n_] := a[n] = Sum[(-1)^(n - k - 1) Binomial[n - 1, k] Sum[a[d], {d, Divisors[k]}], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 28}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 09 2019
STATUS
approved