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A332254
E.g.f.: 1 / (2 - exp(exp(x) - 1 - x)).
0
1, 0, 1, 1, 10, 31, 271, 1534, 14603, 120173, 1310224, 13947517, 175477699, 2265702388, 32673218085, 492565328493, 8053045395018, 138334722101571, 2535114408394699, 48790865853110950, 991843960201311455, 21121971129683138297, 471959969940724275432
OFFSET
0,5
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000296(k) * a(n-k).
a(n) ~ n! * exp(1 - exp(c-1)/2) / ((1 - 2*exp(1-c)) * (c - 1 - log(2))^(n+1)), where c = -LambertW(-1, -exp(-1)/2) = 2.678346990016660653412884512094523... - Vaclav Kotesovec, Feb 08 2020
MATHEMATICA
nmax = 22; CoefficientList[Series[1/(2 - Exp[Exp[x] - 1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) seq(n)={Vec(serlaplace(1/(2 - exp(exp(x + O(x*x^n)) - 1 - x))))} \\ Andrew Howroyd, Feb 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 08 2020
STATUS
approved