A341070 Number of ways to write n as an ordered sum of 10 squarefree numbers.

1, 10, 55, 210, 625, 1552, 3400, 6840, 12960, 23330, 40028, 65740, 104230, 160670, 241640, 354772, 509620, 718980, 999645, 1370720, 1853903, 2476250, 3274110, 4289810, 5568820, 7162184, 9138045, 11579180, 14574755, 18215900, 22619016, 27929990, 34311845, 41921710, 50946945

Offset

10,2

Links

Table of n, a(n) for n=10..44.

Formula

G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^10.

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 10):
seq(a(n), n=10..44);  # Alois P. Heinz, Feb 04 2021

Mathematica

nmax = 44; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

Crossrefs

Cf. A005117, A008683, A008966, A098235, A280210, A326626, A341064, A341065, A341066, A341067, A341068, A341069.

Sequence in context: A337898 A357730 A341989 * A244871 A162617 A341139

Adjacent sequences: A341067 A341068 A341069 * A341071 A341072 A341073

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved