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%I #17 May 21 2023 07:35:53
%S 0,0,0,1,0,0,0,2,1,1,1,3,2,3,3,7,6,8,9,13,13,17,19,28,30,38,43,56,62,
%T 76,87,110,124,151,173,211,241,289,332,399,456,539,620,733,838,983,
%U 1127,1322,1513,1761,2016,2343,2677,3096,3536,4083,4655,5355,6101,7005,7969,9124,10370,11856,13453,15340
%N Number of partitions of n whose least part is a multiple of 4.
%H Vaclav Kotesovec, <a href="/A363095/b363095.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=1} x^(4*k)/Product_{j>=4*k} (1-x^j).
%F a(n) ~ Pi^3 * exp(Pi*sqrt(2*n/3)) / (3 * 2^(5/2) * n^(5/2)) * (1 - (5*sqrt(6)/Pi + 169*Pi*sqrt(6)/144)/sqrt(n)). - _Vaclav Kotesovec_, May 21 2023
%t nmax = 60; Rest[CoefficientList[Series[Sum[x^(4*k)/QPochhammer[x^(4*k), x], {k, 1, nmax/4}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 20 2023 *)
%o (PARI) my(N=70, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(4*k)/prod(j=4*k, N, 1-x^j))))
%Y Cf. A026805, A363094, A363096.
%Y Cf. A363046.
%K nonn
%O 1,8
%A _Seiichi Manyama_, May 19 2023
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