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A375540
a(n) = 2^n * n! * [x^n] (1/2 - exp(-x))^n.
0
1, 2, 12, 126, 1880, 36250, 856212, 23928758, 772172592, 28253043378, 1155731972780, 52265163565582, 2589097062756360, 139428505876012106, 8110011431007355716, 506710228437429986790, 33844577422630735656032, 2406541293179536265812834, 181497377154154817667851100
OFFSET
0,2
FORMULA
a(n) ~ n^n / (sqrt(1+LambertW(-exp(-1)/2)) * exp(n) * (-LambertW(-exp(-1)/2))^n). - Vaclav Kotesovec, Sep 01 2024
MAPLE
gf := n -> (1/2 - exp(-x))^n:
ser := n -> series(gf(n), x, 20):
a := n -> expand(2^n*n!*coeff(ser(n), x, n)):
seq(a(n), n = 0..18);
MATHEMATICA
Table[2^n * n! * SeriesCoefficient[(1/2 - E^(-x))^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 01 2024 *)
CROSSREFS
Sequence in context: A209627 A253282 A375899 * A201470 A349268 A366821
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 01 2024
STATUS
approved