A294351
Product of first n terms of the binomial transform of the number of partitions into distinct parts (A000009).
Original entry on oeis.org
1, 2, 8, 72, 1512, 74088, 8446032, 2238198480, 1376492065200, 1957371716714400, 6404520257089516800, 47989070286371749382400, 820133211194093196945216000, 31862175254890520701321641600000, 2805942463821933705561890367504000000
Offset: 0
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Table[Product[Sum[Binomial[m, k]*PartitionsQ[k], {k, 0, m}], {m, 0, n}], {n, 0, 15}]
A307264
Expansion of (1/(1 - x)) * Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).
Original entry on oeis.org
1, 2, 3, 5, 10, 22, 49, 107, 229, 486, 1035, 2225, 4825, 10508, 22875, 49624, 107154, 230356, 493471, 1054602, 2250850, 4801825, 10244940, 21865466, 46680201, 99659713, 212697816, 453634533, 966551216, 2057052465, 4372660927, 9284272791, 19692591418
Offset: 0
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a:=series((1/(1-x))*mul(1/(1+(-x)^k/(1-x)^k),k=1..100),x=0,33): seq(coeff(a,x,n),n=0..32); # Paolo P. Lava, Apr 03 2019
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nmax = 32; CoefficientList[Series[1/(1 - x) Product[1/(1 + (-x)^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]
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