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a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^prime(k)).
0

%I #4 Apr 13 2018 21:53:39

%S 1,0,2,3,16,30,252,399,4672,8100,111200,193006,3279888,5631093,

%T 114137072,196030350,4600308224,7873377297,210745840824,359490499457,

%U 10808589776800,18389567969010,613522956193532,1041400845949218,38179982045681856,64675343605547500,2584515863960831060

%N a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^prime(k)).

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%t Table[SeriesCoefficient[Product[1/(1 - n x^Prime[k]), {k, 1, n}], {x, 0, n}], {n, 0, 26}]

%Y Cf. A000607, A002098, A124577, A145519, A301971.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 13 2018