A346791 -id:A346791 - cp's OEIS frontend

A346430 E.g.f.: 1 / (1 - x - Sum_{k>=2} prime(k-1) * x^k / k!).

1, 1, 4, 21, 149, 1317, 13985, 173207, 2451807, 39043963, 690844441, 13446183857, 285500221447, 6567135007015, 162678487750465, 4317650962178897, 122234460353464081, 3676789159574231397, 117102826395968235853, 3936834192059910096205, 139316727760914366716635

Offset: 0

Ilya Gutkovskiy, Aug 04 2021

nonn

Cf. A000040, A008578, A030017, A300632, A300662, A302194, A346791.

nmax = 20; CoefficientList[Series[1/(1 - x - Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A008578(k) * a(n-k).

A346792 G.f.: 1 / (1 + x + Sum_{k>=2} prime(k-1) * x^k).

Original entry on oeis.org

1, -1, -1, 0, 0, 1, 0, 3, 1, -1, -4, -10, 3, 0, 9, 19, 9, 2, -44, -27, -40, -3, 95, 75, 156, -36, -181, -274, -349, 81, 205, 982, 832, 35, -596, -2587, -1803, -1259, 2118, 5876, 5365, 4922, -6811, -12175, -17181, -12932, 14144, 28575, 53548, 27663, -19181

Offset: 0

Ilya Gutkovskiy, Aug 04 2021

sign

Cf. A000040, A008578, A030017, A030018, A300662, A346791.

nmax = 50; CoefficientList[Series[1/(1 + x + Sum[Prime[k - 1] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

a(0) = 1; a(n) = -Sum_{k=1..n} A008578(k) * a(n-k).

cp's OEIS Frontend

A346430 E.g.f.: 1 / (1 - x - Sum_{k>=2} prime(k-1) * x^k / k!).

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