A290971 Write x/(1-x) in the form Sum_{j>=1} a(j)*x^j/(1+a(j)*x^j).

1, 2, 0, 6, 0, -6, 0, 54, 0, -30, 0, -114, 0, -126, 0, 4470, 0, -294, 0, -5850, 0, -2046, 0, -92418, 0, -8190, 0, -247674, 0, 2010, 0, 30229110, 0, -131070, 0, -8200914, 0, -524286, 0, -362617770, 0, 183162, 0, -354416634, 0, -8388606, 0, -53614489794, 0

Offset

1,2

Links

Table of n, a(n) for n=1..49.

Formula

a(n) = -Sum_t (-1)^v(t) where the sum is over all same-trees of weight n (see A281145 for definition) and v(t) is the number of nodes (branchings and leaves) in t.

Mathematica

nn=20; -Solve[Table[Sum[a[n/d]^d, {d, Divisors[n]}]==-1, {n, nn}], Array[a, nn]][[1, All, 2]]

Crossrefs

Cf. A048272, A220418, A260685, A273873, A275870, A281145, A289078, A289501, A290261, A290973.

Sequence in context: A275325 A300227 A378791 * A178636 A353276 A046520

Adjacent sequences: A290968 A290969 A290970 * A290972 A290973 A290974

Keyword

sign

Author

Gus Wiseman, Aug 16 2017

Status

approved