A331928 Number of compositions (ordered partitions) of n into distinct proper divisors of n.

1, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 30, 0, 24, 0, 0, 0, 894, 0, 0, 0, 120, 0, 150, 0, 0, 0, 0, 0, 1134, 0, 0, 0, 864, 0, 30, 0, 0, 0, 0, 0, 11934, 0, 0, 0, 0, 0, 150, 0, 840, 0, 0, 0, 129438, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0

Offset

0,7

Links

Table of n, a(n) for n=0..70.

Index entries for sequences related to compositions

Formula

a(n) = A331927(n) - 1 for n > 0.

Example

a(6) = 6 because we have [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 3, 2] and [1, 2, 3].

Prog

(PARI) a(n)={if(n==0, 1, my(v=divisors(n)); subst(serlaplace((0*y) + polcoef(prod(i=1, #v-1, 1 + y*x^v[i] + O(x*x^n)), n)), y, 1))} \\ Andrew Howroyd, Feb 01 2020

Crossrefs

Cf. A018818, A027751, A033630, A065205, A100346, A210442, A211111, A294138, A331927.

Sequence in context: A035322 A270031 A284105 * A228632 A229657 A306550

Adjacent sequences: A331925 A331926 A331927 * A331929 A331930 A331931

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 01 2020

Status

approved