A347545 Number of partitions of n into 9 or more parts.

1, 2, 4, 7, 12, 19, 30, 45, 67, 97, 138, 193, 267, 364, 491, 656, 868, 1139, 1483, 1917, 2461, 3142, 3985, 5030, 6315, 7893, 9817, 12165, 15007, 18451, 22597, 27589, 33565, 40724, 49249, 59410, 71460, 85753, 102632, 122574, 146032, 173638, 206003, 243951, 288296, 340124

Offset: 9

Author

Ilya Gutkovskiy, Sep 06 2021

Keywords

• nonn

Crossrefs

Cf. A000065, A004250, A008638, A035300, A035301, A347542, A347543, A347544, A347547.

Programs

Mathematica

nmax = 54; CoefficientList[Series[Sum[x^k/Product[(1 - x^j), {j, 1, k}], {k, 9, nmax}], {x, 0, nmax}], x] // Drop[#, 9] &

Formula

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