A303906 - OEIS

%I #6 May 04 2018 07:36:03

%S 1,0,0,1,0,0,2,0,0,2,1,0,3,1,0,4,2,0,5,2,1,7,3,1,8,4,2,10,6,2,13,8,3,

%T 15,10,4,20,12,6,22,16,8,28,19,10,33,25,12,40,29,16,48,36,19,55,44,26,

%U 65,53,30,76,64,38,88,75,46,106,88,56,119,105,68,141,122,80,160

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

%C First differences of A007294.

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

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

%F G.f.: 1 + Sum_{j>=2} x^(j*(j+1)/2)/Product_{k=2..j} (1 - x^(k*(k+1)/2)).

%F a(n) ~ exp(3 * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3) / 2) * Zeta(3/2)^(5/3) / (2^(9/2) * sqrt(3) * Pi^(2/3) * n^(13/6)). - _Vaclav Kotesovec_, May 04 2018

%t nmax = 75; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)/2)), {k, 2, nmax}], {x, 0, nmax}], x]

%t nmax = 75; CoefficientList[Series[1 + Sum[x^(j (j + 1)/2)/Product[(1 - x^(k (k + 1)/2)), {k, 2, j}], {j, 2, nmax}], {x, 0, nmax}], x]

%Y Cf. A000217, A002865, A007294, A078134, A302835.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, May 02 2018