%I #4 Mar 21 2018 17:14:51

%S 1,1,3,13,51,201,825,3431,14355,60493,256463,1092268,4669665,20029036,

%T 86148373,371434173,1604845715,6946936628,30121158813,130795358333,

%U 568709929191,2475778867547,10789659781640,47069225185789,205524447217185,898163031782576,3928112419640126

%N a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^n.

%C Number of partitions of n into triangular numbers of n kinds.

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

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%t Table[SeriesCoefficient[Product[1/(1 - x^(k (k + 1)/2))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]

%Y Cf. A000217, A000294, A007294, A008485, A298435, A298730, A300974, A301334.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 21 2018