A302837 a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^prime(k)).
1, 0, 2, 3, 16, 30, 252, 399, 4672, 8100, 111200, 193006, 3279888, 5631093, 114137072, 196030350, 4600308224, 7873377297, 210745840824, 359490499457, 10808589776800, 18389567969010, 613522956193532, 1041400845949218, 38179982045681856, 64675343605547500, 2584515863960831060
Offset: 0
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Mathematica
Table[SeriesCoefficient[Product[1/(1 - n x^Prime[k]), {k, 1, n}], {x, 0, n}], {n, 0, 26}]