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Number of partitions of n into distinct parts, none being 5.
9

%I #22 Apr 21 2021 03:47:45

%S 1,1,1,2,2,2,3,4,4,6,8,9,11,14,16,19,23,27,32,38,45,53,62,72,84,97,

%T 112,130,150,172,199,228,260,298,340,386,440,500,566,642,727,820,926,

%U 1044,1174,1321,1484,1664,1866,2090,2337,2613,2918,3254,3628,4041,4495

%N Number of partitions of n into distinct parts, none being 5.

%H Vincenzo Librandi, <a href="/A015750/b015750.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A015740(n+5). - _Michel Marcus_, Feb 20 2014

%t CoefficientList[Series[Product[1+q^n, {n, 1, 60}]/(1+q^5), {q, 0, 60}], q]

%t Table[Count[Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], x_ /; ! MemberQ[x, 5]], {n, 0, 56}] (* _Robert Price_, May 17 2020 *)

%Y Cf. A025147, A015744, A015745, A015746, A015753, A015754, A015755.

%K nonn

%O 0,4

%A _Clark Kimberling_

%E Corrected and extended by _Dean Hickerson_, Oct 10 2001