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A015743 Number of 8's in all the partitions of n into distinct parts. 2

%I

%S 0,0,0,0,0,0,0,1,1,1,2,2,3,4,5,5,7,9,10,13,15,18,22,27,31,37,44,51,61,

%T 71,82,95,111,128,148,171,195,225,258,295,337,384,437,497,565,639,724,

%U 818,923,1042,1173,1319,1483,1665

%N Number of 8's in all the partitions of n into distinct parts.

%H David A. Corneth, <a href="/A015743/b015743.txt">Table of n, a(n) for n = 1..10000</a> (first 2000 terms from Robert Price)

%F G.f.: x^8*Product_{j>=1} (1+x^j)/(1+x^8). - _Emeric Deutsch_, Apr 17 2006

%e a(11)=2 because in the 12 (=A000009(11)) partitions of 11 into distinct parts, namely [11], [10,1], [9,2], [8,3], [8,2,1], [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2] and [5,3,2,1], altogether we have two parts equal to 8.

%p g:=x^8*product(1+x^j,j=1..60)/(1+x^8): gser:=series(g,x=0,57): seq(coeff(gser,x,n),n=1..54); # _Emeric Deutsch_, Apr 17 2006

%t Table[Count[Flatten@Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], 8], {n, 54}] (* _Robert Price_, Jun 13 2020 *)

%K nonn

%O 1,11

%A _Clark Kimberling_

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Last modified June 24 13:35 EDT 2021. Contains 345416 sequences. (Running on oeis4.)