A375540 a(n) = 2^n * n! * [x^n] (1/2 - exp(-x))^n.

1, 2, 12, 126, 1880, 36250, 856212, 23928758, 772172592, 28253043378, 1155731972780, 52265163565582, 2589097062756360, 139428505876012106, 8110011431007355716, 506710228437429986790, 33844577422630735656032, 2406541293179536265812834, 181497377154154817667851100

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

Adjacent sequences: A375537 A375538 A375539 * A375541 A375542 A375543

Keyword

nonn

Author

Peter Luschny, Sep 01 2024

Status

approved