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%I #7 Dec 11 2020 07:29:50
%S 210,330,852,1826,4207,6595,13548,21479,38905,59000,95953,142843,
%T 231431,324152,487361,683227,1003028,1347337,1907811,2541970,3526314,
%U 4597020,6194948,7969172,10618000,13401580,17424498,21875750,28102737,34685941,43856482,53791587
%N Sum over all partitions lambda of n into 4 distinct parts of Product_{i:lambda} prime(i).
%H Alois P. Heinz, <a href="/A258359/b258359.txt">Table of n, a(n) for n = 10..1000</a>
%p g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
%p `if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
%p , j=0..min(1, n/i)))), x, 5), polynom)
%p end:
%p a:= n-> coeff(g(n$2), x, 4):
%p seq(a(n), n=10..60);
%t g[n_, i_] := g[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[g[n - i j, i - 1] (Prime[i] x)^j, {j, 0, Min[1, n/i]}]]];
%t a[n_] := Coefficient[g[n, n], x, 4];
%t a /@ Range[10, 60] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y Column k=4 of A258323.
%Y Cf. A000040.
%K nonn
%O 10,1
%A _Alois P. Heinz_, May 27 2015
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