A343622 E.g.f.: log(1 + x + Sum_{k>=2} prime(k-1) * x^k / k!).

1, 1, -1, -1, 6, -1, -79, 214, 1378, -11321, -14855, 611932, -1739312, -34374895, 311453831, 1548864398, -42005057494, 66254532775, 5287751144127, -45726542532086, -568193240268798, 12768316133375343, 16933257518347115, -3008868695961855284, 21477836260078982762

Offset: 1

Author

Ilya Gutkovskiy, Aug 04 2021

Keywords

• sign

Crossrefs

Cf. A000040, A007446, A007447, A008578, A300632, A336185, A343623.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Log[1 + x + Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! // Rest

Formula

a(n) = A008578(n) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * A008578(n-k) * k * a(k).