A307321
Expansion of Product_{j>=1} 1/(1 - (-1 + Product_{k>=1} 1/(1 - x^k)^k)^j)^j.
Original entry on oeis.org
1, 1, 6, 30, 143, 660, 3000, 13448, 59696, 262788, 1148738, 4989908, 21551733, 92596511, 395921737, 1685304092, 7143861196, 30163965903, 126895681419, 531986033218, 2222961809367, 9260148591001, 38461580964389, 159302487751844, 658054630483936, 2711429650817356
Offset: 0
-
nmax = 25; CoefficientList[Series[Product[1/(1 - (-1 + Product[1/(1 - x^k)^k, {k, 1, nmax}])^j)^j, {j, 1, nmax}], {x, 0, nmax}], x]
A307566
Expansion of Product_{j>=1} (1 + j*(-1 + Product_{k>=1} (1 + k*x^k))^j).
Original entry on oeis.org
1, 1, 4, 18, 72, 289, 1119, 4301, 16408, 62313, 234914, 879822, 3274623, 12125348, 44707778, 164258803, 601535222, 2195926654, 7990792367, 28985219498, 104811279467, 377875493610, 1358584361039, 4872111113570, 17431266435024, 62229179950735, 221699783190996, 788274748711694
Offset: 0
-
nmax = 27; CoefficientList[Series[Product[(1 + j (-1 + Product[(1 + k x^k), {k, 1, nmax}])^j), {j, 1, nmax}], {x, 0, nmax}], x]
A307571
Expansion of Product_{j>=1} (1 + x^j*Product_{k>=1} (1 + x^k)^(k*j))^j.
Original entry on oeis.org
1, 1, 3, 11, 38, 129, 436, 1445, 4764, 15583, 50667, 163890, 527620, 1691368, 5400754, 17183173, 54487190, 172235992, 542844404, 1706169816, 5348478123, 16724698483, 52174714116, 162399459964, 504402061533, 1563430065203, 4836462927829, 14933470162894, 46026742326000, 141614337715832
Offset: 0
-
nmax = 29; CoefficientList[Series[Product[(1 + x^j Product[(1 + x^k)^(k j), {k, 1, nmax}])^j, {j, 1, nmax}], {x, 0, nmax}], x]
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