A341913 Number of partitions of n into 9 distinct and relatively prime parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 73, 94, 123, 157, 201, 252, 318, 393, 488, 598, 732, 887, 1076, 1291, 1549, 1845, 2194, 2592, 3060, 3589, 4206, 4904, 5708, 6615, 7657, 8824, 10156, 11648, 13338, 15224, 17354, 19720, 22380, 25330, 28629, 32277, 36347, 40829, 45812, 51291, 57358

Offset

45,3

Links

Table of n, a(n) for n=45..97.

Formula

G.f.: Sum_{k>=1} mu(k)* x^(45*k) / Product_{j=1..9} (1 - x^(j*k)).

Mathematica

nmax = 97; CoefficientList[Series[Sum[MoebiusMu[k] x^(45 k)/Product[1 - x^(j k), {j, 1, 9}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 45] &

Crossrefs

Cf. A023022, A023029, A023034, A078374, A101271, A339672, A340719, A341868, A341870, A341912, A341914.

Sequence in context: A309058 A218509 A026815 * A008638 A008632 A347575

Adjacent sequences: A341910 A341911 A341912 * A341914 A341915 A341916

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2021

Status

approved