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
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a(n) = polcoef(prod(k=1, n, x^k+1/x^k)^n, 0);
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a(n) = polcoef(prod(k=1, n, 1+x^(2*k))^n, n^2*(n+1)/2);
A350306
a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^k.
Original entry on oeis.org
1, 1, 3, 57, 2855, 459597, 240485241, 395649695145, 2023017357650345, 31899582278283495743, 1542718311570632349138107, 227912729019868361872929934159, 102547791095886594007005283976727239, 140202209701199998336689204011032887220183
Offset: 0
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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 *)
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a(n) = polcoef(prod(k=1, n, (x^k+1+1/x^k)^k), 0);
A350308
a(n) is the constant term in the expansion of Product_{j=1..n} (Sum_{k=-j..j} x^k)^j.
Original entry on oeis.org
1, 1, 13, 2431, 10027503, 1107781071903, 3893880730064443963, 506016205547402043327062969, 2774765502272595019563619139799271431, 722310089115924894687149792741562790592722949523
Offset: 0
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a[n_] := Coefficient[Series[Product[Sum[x^k, {k, -j, j}]^j, {j, 1, n}], {x, 0, 0}], x, 0]; Array[a, 10, 0] (* Amiram Eldar, Dec 24 2021 *)
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a(n) = polcoef(prod(j=1, n, sum(k=-j, j, x^k)^j), 0);
Showing 1-3 of 3 results.
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