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%I #31 Mar 07 2021 03:55:47
%S 0,2,5,13,23,47,75,131,203,323,477,729,1041,1517,2132,3012,4134,5718,
%T 7713,10453,13918,18538,24357,32037,41612,54040,69538,89362,113925,
%U 145095,183473,231697,290899,364577,454632,566016,701436,867800,1069430,1315550,1612595
%N Sum of all parts > 1 of all partitions of n.
%C Also the total number of missing parts in the partitions of n. A missing part of a partition of n is any number from 1 to n not occurring as a part. For example for n = 3, 1,2 are missing from 3; 3 is missing from 2+1, and 2,3 are missing from 1+1+1, for a total of a(3) = 5. - _George Beck_, Oct 23 2014
%H Alois P. Heinz, <a href="/A194552/b194552.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A066186(n) - A000070(n-1).
%F a(n) = n * A000041(n) - A000070(n-1). - _George Beck_, Oct 24 2014
%F G.f.: (x/(1 - x)) * (d/dx) Product_{k>=2} 1/(1 - x^k). - _Ilya Gutkovskiy_, Mar 06 2021
%p b:= proc(n, i) option remember; local h, t;
%p if n<0 or i<1 then [0, 0]
%p elif n=0 or i=1 then [1, 0]
%p else h:= b(n, i-1); t:= b(n-i, i);
%p [h[1]+t[1], h[2]+t[2] +t[1]*i]
%p fi
%p end:
%p a:= n-> b(n, n)[2]:
%p seq(a(n), n=1..50); # _Alois P. Heinz_, Dec 14 2011
%t a[n_] := n PartitionsP[n] -Total@Table[PartitionsP[k], {k, 0, n - 1}]; a /@ Range[40] (* _George Beck_, Oct 23 2014 *)
%Y Partial sums of A138880.
%Y Cf. A096541, A135010, A138121, A138135.
%K nonn
%O 1,2
%A _Omar E. Pol_, Dec 11 2011
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