A384092 -id:A384092 - cp's OEIS frontend

A384091 a(n) = [x^n] Product_{k=1..n} (1 + k^2*x)^n.

1, 1, 33, 6968, 4503078, 6507545775, 17683339661956, 80849884332530600, 575530003415681613468, 6023356562522188931288775, 88682105895482127774508529242, 1773600518272635675832361778156960, 46830898160739235037404595987069052560, 1594447058825655577475889095097916983404652

Offset: 0

Vaclav Kotesovec, May 19 2025

nonn

Cf. A351507, A001044, A384092.

Table[SeriesCoefficient[Product[(1+k^2*x)^n, {k, 0, n}], {x, 0, n}], {n, 0, 15}]

a(n) ~ exp(n + 3/5) * n^(3*n - 1/2) / (sqrt(2*Pi) * 3^n).

A384093 a(n) = [x^n] Product_{k=1..n} ((1 + k^2x)/(1 - k^2x))^n.

Original entry on oeis.org

1, 2, 200, 100372, 141369600, 429768373550, 2413602498186776, 22580623631512230760, 326908252720653523943424, 6930499895312478999698799930, 206129722171946147890239366225000, 8311703033335976017330775929889992316, 441845483828200905036741829941273994080000

Offset: 0

Vaclav Kotesovec, May 19 2025

nonn

Cf. A384091, A384092.

Cf. A351764, A384043.

Table[SeriesCoefficient[Product[((1+k^2*x)/(1-k^2*x))^n, {k, 1, n}], {x, 0, n}], {n, 0, 15}]

a(n) ~ 2^(n - 1/2) * exp(n + 3/2) * n^(3*n - 1/2) / (sqrt(Pi) * 3^n).

cp's OEIS Frontend

A384091 a(n) = [x^n] Product_{k=1..n} (1 + k^2*x)^n.

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Formula

A384093 a(n) = [x^n] Product_{k=1..n} ((1 + k^2x)/(1 - k^2x))^n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

cp's OEIS Frontend

A384091 a(n) = [x^n] Product_{k=1..n} (1 + k^2*x)^n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A384093 a(n) = [x^n] Product_{k=1..n} ((1 + k^2*x)/(1 - k^2*x))^n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A384093 a(n) = [x^n] Product_{k=1..n} ((1 + k^2x)/(1 - k^2x))^n.