A300417 - OEIS

%I #7 Mar 05 2018 17:24:32

%S 1,2,1,2,4,2,3,6,3,4,10,8,5,10,11,8,14,16,11,18,22,18,23,22,22,34,31,

%T 26,39,40,33,50,56,36,53,74,51,62,86,68,77,98,86,88,102,106,120,130,

%U 120,136,157,134,157,194,155,182,241,194,196,256,237,236,288,282,273,324

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

%C Number of partitions of n into distinct triangular parts (A000217), with 2 types of each part.

%C Self-convolution of A024940.

%H Vaclav Kotesovec, <a href="/A300417/b300417.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>=1} (1 + x^A000217(k))^2.

%F a(n) ~ exp(3*Pi^(1/3) * ((sqrt(2)-1) * Zeta(3/2)/2)^(2/3) * n^(1/3)) * ((sqrt(2)-1) * Zeta(3/2) / (2*Pi))^(1/3) / (4*sqrt(3) * n^(5/6)). - _Vaclav Kotesovec_, Mar 05 2018

%t nmax = 65; CoefficientList[Series[Product[(1 + x^(k (k + 1)/2))^2, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000217, A022567, A024940, A279226, A298435.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Mar 05 2018