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Number of partitions of n into 9 or more parts.
4

%I #5 Sep 06 2021 21:35:13

%S 1,2,4,7,12,19,30,45,67,97,138,193,267,364,491,656,868,1139,1483,1917,

%T 2461,3142,3985,5030,6315,7893,9817,12165,15007,18451,22597,27589,

%U 33565,40724,49249,59410,71460,85753,102632,122574,146032,173638,206003,243951,288296,340124

%N Number of partitions of n into 9 or more parts.

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

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

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

%K nonn

%O 9,2

%A _Ilya Gutkovskiy_, Sep 06 2021