A008485 -id:A008485 - cp's OEIS frontend

A382949 a(n) = [(x*y)^n] Product_{k>=1} 1 / (1 - x^k - y^k)^n.

1, 2, 48, 1190, 33648, 996292, 30626316, 965163166, 30995087312, 1009925740946, 33289934968618, 1107728567917028, 37149902553751260, 1254165186821008126, 42580296599191705276, 1452739684287637542640, 49776378699192072523920, 1711962807156690517057454

Offset: 0

Ilya Gutkovskiy, Apr 09 2025

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Cf. A008485, A322211.

Table[SeriesCoefficient[Product[1/(1 - x^k - y^k)^n, {k, 1, n}], {x, 0, n}, {y, 0, n}], {n, 0, 17}]

a(n) ~ c * d^n / n, where d = 36.5023860624117446261380818... and c = 0.08167564464819257818345... - Vaclav Kotesovec, Apr 10 2025

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Mar 21 2018

nonn

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

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

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

cp's OEIS Frontend

A382949 a(n) = [(x*y)^n] Product_{k>=1} 1 / (1 - x^k - y^k)^n.

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