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A258363 Sum over all partitions lambda of n into 8 distinct parts of Product_{i:lambda} prime(i).

%I A258363 #4 May 27 2015 17:31:46
%S A258363 9699690,11741730,27927900,49533330,98525490,170218830,325872714,
%T A258363 562212782,1032566057,1629661685,2724030632,4284584225,6990871609,
%U A258363 10713813287,17001782121,25600766613,39614085330,58088625761,87187552970,126762441906,186103726454,266554756593
%N A258363 Sum over all partitions lambda of n into 8 distinct parts of Product_{i:lambda} prime(i).
%H A258363 Alois P. Heinz, <a href="/A258363/b258363.txt">Table of n, a(n) for n = 36..1000</a>
%p A258363 g:= proc(n, i) option remember; convert(series(`if`(n=0, 1,
%p A258363       `if`(i<1, 0, add(g(n-i*j, i-1)*(ithprime(i)*x)^j
%p A258363       , j=0..min(1, n/i)))), x, 9), polynom)
%p A258363     end:
%p A258363 a:= n-> coeff(g(n$2), x, 8):
%p A258363 seq(a(n), n=36..60);
%Y A258363 Column k=8 of A258323.
%Y A258363 Cf. A000040.
%K A258363 nonn
%O A258363 36,1
%A A258363 _Alois P. Heinz_, May 27 2015