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%I #7 Dec 11 2020 07:30:46
%S 2310,2730,7860,15606,35594,67255,120061,201324,364479,592991,1004771,
%T 1530056,2444073,3691392,5610179,8334486,12213775,17529361,25187765,
%U 35345858,49999364,68516285,94223007,127478773,172613052,230362430,305639795,401637665,527011287
%N Sum over all partitions lambda of n into 5 distinct parts of Product_{i:lambda} prime(i).
%H Alois P. Heinz, <a href="/A258360/b258360.txt">Table of n, a(n) for n = 15..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, 6), polynom)
%p end:
%p a:= n-> coeff(g(n$2), x, 5):
%p seq(a(n), n=15..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, 5];
%t a /@ Range[15, 60] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y Column k=5 of A258323.
%Y Cf. A000040.
%K nonn
%O 15,1
%A _Alois P. Heinz_, May 27 2015
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