A369578 -id:A369578 - cp's OEIS frontend

A383073 a(n) = [x^n] Product_{k=1..n} (1 + x^k)^binomial(n,k).

1, 1, 2, 11, 69, 552, 5133, 53804, 626440, 7979043, 110074741, 1631532542, 25813521836, 433619035254, 7698641650937, 143908414079881, 2822753485000135, 57930283521990154, 1240695879627856673, 27666701629865989070, 641049490249340264699

Offset: 0

Vaclav Kotesovec, Apr 15 2025

nonn

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

Cf. A360660.

Cf. A026007, A102866, A344130, A369578.

Table[SeriesCoefficient[Product[(1 + x^k)^Binomial[n, k], {k, 1, n}], {x, 0, n}], {n, 0, 20}]

A361805 Expansion of Product_{j=1..n, k=1..n} (1 + x^(k^j)) / (1 - x^(k^j)).

Original entry on oeis.org

1, 2, 10, 52, 278, 1508, 8262, 45604, 253186, 1412196, 7906866, 44411420, 250124308, 1411963200, 7986664250, 45255888828, 256840959728, 1459686175768, 8306130772008, 47318321533008, 269839722667800, 1540242835509060, 8799238591245006, 50308756959106988

Offset: 0

Vaclav Kotesovec, Jan 28 2024

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Cf. A369577, A369578.
Cf. A015128, A103265, A280263.
Cf. A000041, A001156, A003108.
Cf. A000009, A033461, A279329.

Table[SeriesCoefficient[Product[Product[(1+x^(k^j))/(1-x^(k^j)), {k, 1, n^(1/j)}], {j, 1, n}], {x, 0, n}], {n, 0, 40}]

a(n) ~ c * (1 + sqrt(2))^(2*n) / sqrt(n), where c = 0.6431307610999754935775134585988078560575016233514072350040712130921818...

cp's OEIS Frontend

A383073 a(n) = [x^n] Product_{k=1..n} (1 + x^k)^binomial(n,k).

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