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A345758
E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k)^(1/k!).
3
1, -1, -2, -2, 4, 63, 448, 2490, 14733, 109151, 790418, 5861623, 91442844, 1857444743, 27708811583, 336714649323, 6016551711313, 167673369006642, 4183443404331446, 82140898773966502, 1493427665082817617, 37403762698805913754, 1340432910567030307828
OFFSET
0,3
COMMENTS
Stirling transform of A345762.
LINKS
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Stirling Transform
FORMULA
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).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1-(exp(x)-1)^k)^(1/k!))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, (exp((exp(x)-1)^k)-1)/k))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 26 2021
STATUS
approved