A384043
a(n) = [x^n] Product_{k=1..n} (1 + k^2*x) / (1 - k^2*x).
Original entry on oeis.org
1, 2, 50, 4188, 735600, 221302710, 101667388082, 66218673102680, 58048466179356672, 65901249246347377770, 94061755750395244537250, 164863945136411230998746612, 348110204753572939058548570000, 871547135491620353615820806025918, 2552918049709989779004770502542335650
Offset: 0
-
Table[SeriesCoefficient[Product[(1+k^2*x)/(1-k^2*x), {k, 1, n}], {x, 0, n}], {n, 0, 15}]
A384044
a(n) = [x^n] Product_{k=1..n} (1 + k^3*x) / (1 - k^3*x).
Original entry on oeis.org
1, 2, 162, 75672, 104312000, 317309605650, 1803288012589602, 17180843554017736544, 254292459616733559570432, 5525508321588276184345621650, 168733575675064578625834983478850, 6994229599670887851052241626545021912, 382562895157136117988572795915676719695680
Offset: 0
-
Table[SeriesCoefficient[Product[(1+k^3*x)/(1-k^3*x), {k, 1, n}], {x, 0, n}], {n, 0, 12}]
A384086
a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^2.
Original entry on oeis.org
1, 4, 72, 2352, 112000, 7023540, 546991704, 50923706176, 5517464159232, 682067031126660, 94744306830613000, 14610279918692775504, 2476682373835289303424, 457771369968515293229812, 91624876032673265663215800, 19743379886572250897986694400, 4556982707091255612929249419264
Offset: 0
-
Table[SeriesCoefficient[Product[(1+k*x)^2/(1-k*x)^2, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
A384087
a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^3.
Original entry on oeis.org
1, 6, 162, 7848, 552000, 51035310, 5853933666, 802178739936, 127879052859648, 23252775004089990, 4750089647035004250, 1077069265550569663416, 268437124701985949614944, 72940650531961450912140558, 21461129870889481564510048050, 6797577340761206051865208521600, 2306127185536355501260494657447936
Offset: 0
-
Table[SeriesCoefficient[Product[(1+k*x)^3/(1-k*x)^3, {k, 1, n}], {x, 0, n}], {n, 0, 16}]
A384088
a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^4.
Original entry on oeis.org
1, 8, 288, 18528, 1728000, 211687080, 32159822688, 5835397918336, 1231573968949248, 296447550279133320, 80158746419240852000, 24057027574081163030688, 7935414295799696292767232, 2853706409310576479751168168, 1111199574070700473937862463200, 465782420445680979210397280524800
Offset: 0
-
Table[SeriesCoefficient[Product[(1+k*x)^4/(1-k*x)^4, {k, 1, n}], {x, 0, n}], {n, 0, 16}]
A384093
a(n) = [x^n] Product_{k=1..n} ((1 + k^2*x)/(1 - k^2*x))^n.
Original entry on oeis.org
1, 2, 200, 100372, 141369600, 429768373550, 2413602498186776, 22580623631512230760, 326908252720653523943424, 6930499895312478999698799930, 206129722171946147890239366225000, 8311703033335976017330775929889992316, 441845483828200905036741829941273994080000
Offset: 0
-
Table[SeriesCoefficient[Product[((1+k^2*x)/(1-k^2*x))^n, {k, 1, n}], {x, 0, n}], {n, 0, 15}]
Showing 1-6 of 6 results.