A350305
a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^n.
Original entry on oeis.org
1, 1, 13, 1437, 1884211, 24657701475, 3111336932350947, 3710920324904591897521, 41323213770479673319301068309, 4261037235228828189774620497534270303, 4045313784246510024420372971256850718016451185
Offset: 0
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f:= n -> coeff(mul(x^k+1+1/x^k,k=1..n)^n,x,0):
map(f, [$0..12]); # Robert Israel, Jan 15 2023
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a[n_] := Coefficient[Series[Product[(x^k + 1 + 1/x^k)^n, {k, 1, n}], {x, 0, 0}], x, 0]; Array[a, 11, 0] (* Amiram Eldar, Dec 24 2021 *)
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a(n) = polcoef(prod(k=1, n, x^k+1+1/x^k)^n, 0);
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a(n) = polcoef(prod(k=1, n, 1+x^k+x^(2*k))^n, n^2*(n+1)/2);
A369372
a(n) is the constant term in expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^3.
Original entry on oeis.org
1, 7, 85, 1437, 26707, 534513, 11255951, 245612031, 5503639327, 125900330437, 2928092906281, 69026845135479, 1645689594867257, 39611576627651927, 961279033420170871, 23494000801494204647, 577777092945262623161, 14287061769367391787065, 355010279665452190629001
Offset: 0
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Table[Coefficient[Product[(x^k + 1 + 1/x^k)^3, {k, 1, n}], x, 0], {n, 0, 18}]
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a(n) = polcoef(prod(k=1, n, (x^k + 1 + 1/x^k)^3), 0); \\ Michel Marcus, Jan 22 2024
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
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Table[Coefficient[Product[(x^k + 1 + 1/x^k)^4, {k, 1, n}], x, 0], {n, 0, 16}]
A369386
a(n) is the constant term in expansion of Product_{k=1..n} (x^(2*k-1) + 1/x^(2*k-1))^2.
Original entry on oeis.org
1, 2, 4, 8, 18, 48, 138, 428, 1392, 4652, 15884, 55124, 193724, 688008, 2465134, 8899700, 32342236, 118215780, 434314138, 1602935104, 5940303754, 22095769648, 82464791420, 308715131744, 1158949678600, 4362040367048, 16456820491806, 62223707844096
Offset: 0
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Table[Coefficient[Product[(x^(2 k - 1) + 1/x^(2 k - 1))^2, {k, 1, n}], x, 0], {n, 0, 27}]
A369387
a(n) is the constant term in expansion of Product_{k=1..n} (x^(2*k-1) + 1 + 1/x^(2*k-1))^2.
Original entry on oeis.org
1, 3, 9, 43, 243, 1539, 10557, 75595, 558117, 4218077, 32466849, 253624579, 2005655781, 16024596491, 129159081787, 1048931938309, 8574963650419, 70507361919587, 582730070295737, 4838280518142269, 40336851095845719, 337541054046113077, 2834101218805540871
Offset: 0
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Table[Coefficient[Product[(x^(2 k - 1) + 1 + 1/x^(2 k - 1))^2, {k, 1, n}], x, 0], {n, 0, 22}]
A369388
a(n) is the constant term in expansion of Product_{k=1..n} (x^prime(k) + 1 + 1/x^prime(k))^2.
Original entry on oeis.org
1, 3, 9, 45, 249, 1373, 9177, 62257, 453179, 3320531, 24087877, 183643865, 1394580343, 10794949627, 85730722969, 686171829489, 5487361175591, 43981108061647, 358362244544957, 2922625435214613, 24006575088945973, 199229783030494775, 1653790732247194785
Offset: 0
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Table[Coefficient[Product[(x^Prime[k] + 1 + 1/x^Prime[k])^2, {k, 1, n}], x, 0], {n, 0, 22}]
A369389
a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^2) + 1 + 1/x^(k^2))^2.
Original entry on oeis.org
1, 3, 9, 35, 141, 745, 3955, 23985, 155527, 1060941, 7393765, 53041015, 387815175, 2882682967, 21715452927, 165583974835, 1275674593889, 9918184576835, 77738274996385, 613753581566079, 4877383708962749, 38989308129231703, 313354624116918229, 2530796548734844153
Offset: 0
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Table[Coefficient[Product[(x^(k^2) + 1 + 1/x^(k^2))^2, {k, 1, n}], x, 0], {n, 0, 23}]
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