A325303 a(1) = 1; a(n+1) = -Sum_{d|n} a(n/d) * a(d).

1, -1, 2, -4, 7, -14, 32, -64, 120, -244, 502, -1004, 1996, -3992, 8048, -16124, 32104, -64208, 128712, -257424, 514416, -1028960, 2058924, -4117848, 8233832, -16467713, 32939418, -65879316, 131750904, -263501808, 527020884, -1054041768, 2108050776, -4216103560, 8432271328

Offset

1,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..3000

Formula

a(n) ~ -(-1)^n * c * 2^n, where c = 0.245410823583396667908354210407104718986708517177206856531763635090205896729... - Vaclav Kotesovec, Sep 09 2019

Mathematica

a[n_] := a[n] = -Sum[a[(n - 1)/d] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 35}]

Prog

(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=1, #v-1, v[n+1] = -sumdiv(n, d, v[d]*v[n/d])); v} \\ Andrew Howroyd, Sep 05 2019

Crossrefs

Cf. A038044, A122698.

Sequence in context: A202973 A372265 A074663 * A356781 A113122 A296984

Adjacent sequences: A325300 A325301 A325302 * A325304 A325305 A325306

Keyword

sign

Author

Ilya Gutkovskiy, Sep 05 2019

Status

approved