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

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

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A137982 A193364 A074509 * A282705 A282704 A276746

Adjacent sequences: A343620 A343621 A343622 * A343624 A343625 A343626

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 04 2021

Status

approved