A336185 -id:A336185 - cp's OEIS frontend

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

Ilya Gutkovskiy, Aug 04 2021

sign

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

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

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

A343623 E.g.f.: -log(1 - x - Sum_{k>=2} prime(k-1) * x^k / k!).

Original entry on oeis.org

1, 3, 11, 59, 416, 3683, 39093, 484220, 6854176, 109150227, 1931303809, 37589753206, 798135918850, 18358887315769, 454779141016707, 12070296596154136, 341715021307029876, 10278722402921420619, 327369178071821161755, 11005696560250745851048, 389469699942038630639524

Offset: 1

Ilya Gutkovskiy, Aug 04 2021

nonn

Cf. A000040, A007446, A007447, A008578, A300632, A336185, A343622.

nmax = 21; CoefficientList[Series[-Log[1 - x - Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! // Rest

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

cp's OEIS Frontend

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

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