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%I #14 Jan 24 2024 18:32:58
%S 1,2,2,4,5,7,10,14,17,25,32,41,54,71,88,115,144,182,229,287,353,443,
%T 545,670,822,1009,1224,1495,1809,2189,2641,3182,3813,4580,5470,6528,
%U 7773,9248,10960,12994,15355,18129,21363,25146,29525,34659,40589,47488,55473
%N Number of partitions p of n such that 2*min(p) is not a part of p.
%C a(n) is also the number of partitions of n with a part whose multiplicity is greater than half the total number of parts. - _Andrew Howroyd_, Jan 17 2024
%H Vaclav Kotesovec, <a href="/A238594/b238594.txt">Table of n, a(n) for n = 1..10000</a> (using data from A238589)
%F a(n) = A000041(n) - A238589(n).
%F a(n) ~ Pi * exp(Pi*sqrt(2*n/3)) / (3*2^(3/2)*n^(3/2)). - _Vaclav Kotesovec_, Jun 09 2021
%F a(n) = Sum_{k>=1} x^(2*k-2)*(1 + x - x^(k-1))/(Product_{j=1..k} (1 - x^j)). - _Andrew Howroyd_, Jan 17 2024
%e a(6) counts all 11 partitions of 6 except these: 42, 321, 2211, 21111.
%t Table[Count[IntegerPartitions[n], p_ /; !MemberQ[p, 2*Min[p]]], {n, 50}]
%o (PARI) seq(n) = {Vec(sum(k=1, n\2+1, x^(2*k-2)*(1 + x - x^(k-1))/prod(j=1, k, 1 - x^j, 1 + O(x^(n-2*k+3))), O(x*x^n)))} \\ _Andrew Howroyd_, Jan 17 2024
%Y Cf. A238589, A325535.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Mar 01 2014
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