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

0,3

Comments

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

Links

Table of n, a(n) for n=0..26.

Index entries for sequences related to partitions

Index to sequences related to polygonal numbers

Mathematica

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

Crossrefs

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

Sequence in context: A370246 A370272 A304629 * A371837 A244784 A197074

Adjacent sequences: A301455 A301456 A301457 * A301459 A301460 A301461

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 21 2018

Status

approved