A321384 a(1) = 1; a(n+1) = -Sum_{d|n} d*a(d).

1, -1, 1, -4, 17, -86, 514, -3599, 28809, -259285, 2592766, -28520427, 342245654, -4449193503, 62288705445, -934330581764, 14949289337033, -254137918729562, 4574482536873349, -86915168200593632, 1738303364014465422, -36504370644303777464, 803096154174654583783, -18471211546017055427010

Offset

1,4

Links

Seiichi Manyama, Table of n, a(n) for n = 1..450

Formula

L.g.f.: log(Product_{n>=1} (1 - x^n)^a(n)) = Sum_{n>=1} a(n+1)*x^n/n.

a(n) ~ -(-1)^n * c * (n-1)!, where c = 0.7144978951771230847588633755835851845867260778566988217176856019246992... - Vaclav Kotesovec, Nov 09 2018

Mathematica

a[1] = 1; a[n_] := a[n] = -Sum[d a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 24}]

Prog

(PARI) a(n) = if (n==1, 1, -sumdiv(n-1, d, d*a(d))); \\ Michel Marcus, Nov 09 2018

Crossrefs

Cf. A281487, A318372.

Sequence in context: A081052 A020074 A163071 * A056542 A331158 A110508

Adjacent sequences: A321381 A321382 A321383 * A321385 A321386 A321387

Keyword

sign

Author

Ilya Gutkovskiy, Nov 08 2018

Status

approved