A300276 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + x^n)^n.

1, 1, 4, 6, 15, 22, 48, 75, 137, 218, 384, 593, 1003, 1549, 2501, 3857, 6110, 9256, 14408, 21675, 33081, 49422, 74483, 110135, 164116, 240955, 355027, 517553, 755893, 1093649, 1584518, 2277986, 3274887, 4679619, 6682635, 9491959, 13471238, 19030370, 26849913, 37734570

Offset

1,3

Comments

Moebius transform of A026007.

Links

Table of n, a(n) for n=1..40.

N. J. A. Sloane, Transforms

Formula

a(n) = Sum_{d|n} mu(n/d)*A026007(d).

Mathematica

nn = 40; f[x_] := 1 + Sum[a[n] x^n/(1 - x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Product[(1 + x^n)^n, {n, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
s[n_] := SeriesCoefficient[Product[(1 + x^k)^k, {k, 1, n}], {x, 0, n}]; a[n_] := Sum[MoebiusMu[n/d] s[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 40}]

Crossrefs

Cf. A000837, A026007, A078374, A300274, A300275, A300277, A300278.

Sequence in context: A100911 A346297 A034765 * A109731 A369437 A027631

Adjacent sequences: A300273 A300274 A300275 * A300277 A300278 A300279

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 01 2018

Status

approved