A350305 -id:A350305 - cp's OEIS frontend

A350306 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^k.

1, 1, 3, 57, 2855, 459597, 240485241, 395649695145, 2023017357650345, 31899582278283495743, 1542718311570632349138107, 227912729019868361872929934159, 102547791095886594007005283976727239, 140202209701199998336689204011032887220183

Offset: 0

Seiichi Manyama, Dec 23 2021

nonn

Cf. A350283, A350305, A350308.

a[n_] := Coefficient[Series[Product[(x^k + 1 + 1/x^k)^k, {k, 1, n}], {x, 0, 0}], x, 0]; Array[a, 14, 0] (* Amiram Eldar, Dec 24 2021 *)

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

A350307 a(n) is the constant term in the expansion of Product_{j=1..n} (Sum_{k=-j..j} x^k)^n.

Original entry on oeis.org

1, 1, 37, 100683, 42935363305, 4440604747662968975, 161247684066768055445081543753, 2819198261291991623302749353791096334609249, 31233334332507494719367656927521237896029724037781845363309

Offset: 0

Seiichi Manyama, Dec 23 2021

nonn

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

Cf. A128081, A128083, A350282, A350305, A350308.

a[n_] := Coefficient[Series[Product[Sum[x^k, {k, -j, j}]^n, {j, 1, n}], {x, 0, 0}], x, 0]; Array[a, 9, 0] (* Amiram Eldar, Dec 24 2021 *)

a(n) = polcoef(prod(j=1, n, sum(k=-j, j, x^k))^n, 0);

a(n) = polcoef(prod(j=1, n, sum(k=0, 2*j, x^k))^n, n^2*(n+1)/2);

cp's OEIS Frontend

A350306 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^k.

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A350307 a(n) is the constant term in the expansion of Product_{j=1..n} (Sum_{k=-j..j} x^k)^n.

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Mathematica

PARI

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