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A258365 Sum over all partitions lambda of n into 10 distinct parts of Product_{i:lambda} prime(i).

%I A258365 #4 May 27 2015 17:36:35
%S A258365 6469693230,6915878970,16974457500,30110390310,56648021430,
%T A258365 91846692630,166537585410,268444482090,465147702876,769400170732,
%U A258365 1299770760139,1975738341511,3175348256422,4843294699465,7521662925183,11300032117575,17213602502741,25375081790449
%N A258365 Sum over all partitions lambda of n into 10 distinct parts of Product_{i:lambda} prime(i).
%H A258365 Alois P. Heinz, <a href="/A258365/b258365.txt">Table of n, a(n) for n = 55..1000</a>
%p A258365 g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
%p A258365       `if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
%p A258365       , j=0..min(1, n/i)))), x, 11), polynom)
%p A258365     end:
%p A258365 a:= n-> coeff(g(n$2), x, 10):
%p A258365 seq(a(n), n=55..75);
%Y A258365 Column k=10 of A258323.
%Y A258365 Cf. A000040.
%K A258365 nonn
%O A258365 55,1
%A A258365 _Alois P. Heinz_, May 27 2015