A303905 - OEIS

%I #6 May 04 2018 07:26:52

%S 1,2,2,3,4,4,5,6,6,7,9,10,10,11,12,13,15,16,17,19,20,22,24,24,26,29,

%T 30,31,34,36,37,41,44,44,47,50,52,56,59,62,65,67,70,73,75,79,85,89,91,

%U 96,100,102,108,113,116,123,129,132,137,142,147,153,158,162,169,176,182,190,196,201

%N Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(k*(k+1)/2)).

%C Partial sums of A024940.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) ~ exp(3 * Pi^(1/3) * ((sqrt(2) - 1) * Zeta(3/2))^(2/3) * n^(1/3) / 2^(4/3)) / (2^(1/3) * (sqrt(2) - 1)^(1/3) * sqrt(3) * Pi^(2/3) * Zeta(3/2)^(1/3) * n^(1/6)). - _Vaclav Kotesovec_, May 04 2018

%t nmax = 69; CoefficientList[Series[1/(1 - x) Product[1 + x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000217, A024940, A036469, A038348, A061208, A248801, A302835, A303668.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, May 02 2018