A307323
Expansion of Product_{j>=1} (1 + (-1 + Product_{k>=1} (1 + x^k)^k)^j)^j.
Original entry on oeis.org
1, 1, 4, 18, 74, 303, 1206, 4741, 18466, 71463, 274879, 1051509, 4001727, 15157935, 57170668, 214787989, 804049797, 2999846236, 11156943967, 41370989836, 152973793900, 564117250793, 2074959664189, 7613615954760, 27871659379578, 101805487967357, 371072295698710
Offset: 0
-
nmax = 26; CoefficientList[Series[Product[(1 + (-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^j)^j, {j, 1, nmax}], {x, 0, nmax}], x]
A307494
Expansion of Product_{j>=1} 1/(1 - j*(-1 + Product_{k>=1} 1/(1 - k*x^k))^j).
Original entry on oeis.org
1, 1, 6, 30, 145, 680, 3151, 14394, 65217, 293223, 1310255, 5820697, 25725139, 113161286, 495659656, 2162471602, 9399682398, 40716499477, 175798072996, 756709512011, 3247830724594, 13901967775738, 59352638426839, 252778786749676, 1074061758972744, 4553583433874616, 19264461634793094
Offset: 0
-
nmax = 26; CoefficientList[Series[Product[1/(1 - j (-1 + Product[1/(1 - k x^k), {k, 1, nmax}])^j), {j, 1, nmax}], {x, 0, nmax}], x]
A307570
Expansion of Product_{j>=1} 1/(1 - x^j*Product_{k>=1} 1/(1 - x^k)^(k*j))^j.
Original entry on oeis.org
1, 1, 4, 15, 58, 215, 789, 2850, 10219, 36330, 128383, 450997, 1576384, 5484086, 18997492, 65547958, 225329592, 771920515, 2635815051, 8972752531, 30456389557, 103095375148, 348071445217, 1172252449310, 3938655968745, 13203699803684, 44167916497886, 147442143911193, 491220771388477
Offset: 0
-
nmax = 28; CoefficientList[Series[Product[1/(1 - x^j Product[1/(1 - x^k)^(k j), {k, 1, nmax}])^j, {j, 1, nmax}], {x, 0, nmax}], x]
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