A345756 -id:A345756 - cp's OEIS frontend

A345758 E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k)^(1/k!).

1, -1, -2, -2, 4, 63, 448, 2490, 14733, 109151, 790418, 5861623, 91442844, 1857444743, 27708811583, 336714649323, 6016551711313, 167673369006642, 4183443404331446, 82140898773966502, 1493427665082817617, 37403762698805913754, 1340432910567030307828

Offset: 0

Seiichi Manyama, Jun 26 2021

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Stirling transform of A345762.

N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Stirling Transform

Cf. A048993, A345756, A345757, A345762.

my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1-(exp(x)-1)^k)^(1/k!))))

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, (exp((exp(x)-1)^k)-1)/k))))

E.g.f.: exp( -Sum_{k>=1} (exp((exp(x) - 1)^k) - 1)/k ).

a(n) = Sum_{k=0..n} Stirling2(n,k) * A345762(k).

A345757 E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k!).

Original entry on oeis.org

1, 1, 2, 8, 34, 137, 614, 3754, 25449, 82747, -1523792, -34833005, -335209288, 194665837, 59685834069, 715582325511, -10186972407657, -584687267399246, -10975484551366964, 8845584310341044, 8145484883568515927, 330326712925212377392, 7816903733527799885488

Offset: 0

Seiichi Manyama, Jun 26 2021

sign

Stirling transform of A298906.

N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Stirling Transform

Cf. A048993, A298906, A345756, A345758.

my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+(exp(x)-1)^k)^(1/k!))))

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (-1)^(k+1)*(exp((exp(x)-1)^k)-1)/k))))

E.g.f.: exp( Sum_{k>=1} (-1)^(k+1) * (exp((exp(x) - 1)^k) - 1)/k ).

a(n) = Sum_{k=0..n} Stirling2(n,k) * A298906(k).

cp's OEIS Frontend

A345758 E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k)^(1/k!).

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A345757 E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k!).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

PARI

Formula