A124996 -id:A124996 - cp's OEIS frontend

A124995 a(n) is the constant term in expansion of Product_{ k = 1..n } (x^k + 1/x^k)^3.

1, 0, 0, 62, 332, 0, 0, 80006, 531524, 0, 0, 173607568, 1226700784, 0, 0, 455805857978, 3321800235936, 0, 0, 1325490660318216, 9841000101286172, 0, 0, 4108826483323392880, 30886378286619335592, 0, 0, 13306426381421174346512, 100916492010297213463566

Offset: 0

N. J. A. Sloane, Jul 12 2008

nonn

From Robert Israel, Nov 09 2017: (Start)
a(n) is the coefficient of x^(3*n*(n+1)/2) in Product_{k=0..n} (x^(2*k)+1)^3.
a(n) = 0 if n == 1 or 2 (mod 4). (End)

Ray Chandler, Table of n, a(n) for n = 0..1114 (terms < 10^1000)
Ovidiu Bagdasar and Dorin Andrica, New results and conjectures on 2-partitions of multisets, 2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO).

For constant term in expansion of Product_{ k = 1..n } (x^k + 1/x^k)^q for other values of q see A063865, A047653, A124996.

seq(coeff(mul(x^k+1/x^k,k=1..n)^3,x,0),n=0..50); # Robert Israel, Nov 09 2017

a(n) = polcoef(prod(k=1, n, (x^k + 1/x^k)^3), 0); \\ Michel Marcus, Jan 07 2021

A350282 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^n.

Original entry on oeis.org

1, 0, 4, 62, 4658, 0, 2319512420, 14225426190522, 361926393013029354, 0, 16231015449888734994721650504, 28330316118212024049511095643949434, 200866780133770636272812495083578779133456, 0

Offset: 0

Seiichi Manyama, Dec 23 2021

nonn

a(n) is the coefficient of x^(n^2 * (n+1)/2) in Product_{k=0..n} (1 + x^(2*k))^n.

Seiichi Manyama, Table of n, a(n) for n = 0..50

Cf. A063865, A047653, A124995, A124996.

Cf. A350283.

a(n) = polcoef(prod(k=1, n, x^k+1/x^k)^n, 0);

a(n) = polcoef(prod(k=1, n, 1+x^(2*k))^n, n^2*(n+1)/2);

a(4*n+1) = 0.

A369373 a(n) is the constant term in expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^4.

Original entry on oeis.org

1, 19, 701, 33873, 1884211, 113091013, 7138569079, 466998324373, 31378587089717, 2152644125539205, 150149036955370989, 10616242785424087153, 759159709650751045807, 54809160248598728775119, 3989668904561505824038609, 292488794939698331845055779, 21576667915867159070829849217

Offset: 0

Ilya Gutkovskiy, Jan 21 2024

nonn

Cf. A007576, A124996, A156181, A369372.

Table[Coefficient[Product[(x^k + 1 + 1/x^k)^4, {k, 1, n}], x, 0], {n, 0, 16}]

cp's OEIS Frontend

A124995 a(n) is the constant term in expansion of Product_{ k = 1..n } (x^k + 1/x^k)^3.

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A350282 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^n.

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A369373 a(n) is the constant term in expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^4.

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