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%I #10 Dec 08 2020 11:40:03
%S 1,0,2,3,5,11,17,32,51,91,144,241,386,618,981,1540,2400,3711,5710,
%T 8699,13217,19917,29891,44593,66244,97888,144072,211097,308061,447833,
%U 648578,935941,1345985,1929291,2756440,3926259,5575720,7895519,11149261,15701660,22054901,30900798,43188113
%N Expansion of Product_{k>=2} (1 + x^k)^k.
%C Number of partitions of n into distinct parts > 1, where n different parts of size n (beginning at 2) are available (2a, 2b, 3a, 3b, 3c, 4a, 4b, 4c, 4d, ...).
%C Convolution of the sequences A026007 and A033999.
%H Seiichi Manyama, <a href="/A298598/b298598.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=2} (1 + x^k)^k.
%F From _Vaclav Kotesovec_, Apr 08 2018: (Start)
%F a(n) + a(n+1) = A026007(n+1).
%F a(n) ~ Zeta(3)^(1/6) * exp((3/2)^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(7/4) * 3^(1/3) * sqrt(Pi) * n^(2/3)). (End)
%t nmax = 42; CoefficientList[Series[Product[(1 + x^k)^k, {k, 2, nmax}], {x, 0, nmax}], x]
%Y Cf. A025147, A026007, A191659.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 22 2018
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