A374364 Expansion of e.g.f. exp( x - Sum_{k>=1} x^(2^k)/2^k ).

1, 1, 0, -2, -8, -24, 16, 400, -3072, -38528, -18944, 1287936, 17843200, 149045248, -188786688, -12007184384, -1265929355264, -20275964313600, 3871935889408, 2355175169523712, 45658709327609856, 565591105847689216, -1448855443865600000

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..200

Formula

E.g.f.: Product_{k>=1} (1 + x^(2*k-1))^(mu(2*k-1)/(2*k-1)), where mu() is the Moebius function.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-sum(k=1, ceil(log(N+1)/log(2)), x^2^k/2^k))))

Crossrefs

Cf. A005388, A008683, A117209, A293604.

Sequence in context: A072842 A303861 A138387 * A354176 A007346 A062247

Adjacent sequences: A374361 A374362 A374363 * A374365 A374366 A374367

Keyword

sign

Author

Seiichi Manyama, Jul 06 2024

Status

approved