A301458 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^n.

1, 1, 3, 13, 51, 201, 825, 3431, 14355, 60493, 256463, 1092268, 4669665, 20029036, 86148373, 371434173, 1604845715, 6946936628, 30121158813, 130795358333, 568709929191, 2475778867547, 10789659781640, 47069225185789, 205524447217185, 898163031782576, 3928112419640126

Offset: 0

Author

Ilya Gutkovskiy, Mar 21 2018

Keywords

• nonn

Comments

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

Links

• Index entries for sequences related to partitions
• Index to sequences related to polygonal numbers

Crossrefs

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

Programs

Mathematica

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