A303907 - OEIS

%I #8 May 04 2018 08:33:53

%S 1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,1,1,0,2,0,0,2,1,0,1,2,0,1,3,0,0,

%T 3,0,2,2,1,2,1,1,2,1,1,3,3,1,1,4,0,2,4,1,2,5,1,2,3,2,3,3,2,2,5,2,4,4,

%U 2,3,6,1,3,6,3,3,7,2,2,7,3,5,6,5,4,6,4,5,5,5,4,10,4,3,11,3

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

%C Number of partitions of n into distinct triangular numbers > 1.

%H Vaclav Kotesovec, <a href="/A303907/b303907.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k)*A024940(k).

%F a(n) ~ exp(3*Pi^(1/3) * ((sqrt(2)-1)*Zeta(3/2))^(2/3) * n^(1/3) / 2^(4/3)) * ((sqrt(2)-1)*Zeta(3/2))^(1/3) / (2^(8/3) * sqrt(3) * Pi^(1/3) * n^(5/6)). - _Vaclav Kotesovec_, May 04 2018

%t nmax = 95; CoefficientList[Series[Product[1 + x^(k (k + 1)/2), {k, 2, nmax}], {x, 0, nmax}], x]

%Y Cf. A000217, A024940, A025147, A280129, A303906.

%K nonn

%O 0,22

%A _Ilya Gutkovskiy_, May 02 2018