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A341979 Number of partitions of n into 8 distinct primes (counting 1 as a prime).

%I A341979 #9 Feb 24 2022 09:58:12
%S A341979 1,0,1,0,0,0,2,0,1,0,1,0,4,0,3,0,3,1,7,0,6,1,6,1,11,0,11,2,11,3,19,1,
%T A341979 18,3,18,5,30,4,28,6,30,10,45,6,40,11,46,16,63,11,60,19,69,25,88,18,
%U A341979 86,32,97,36,121,32,123,47,131,55,164,49,164,69,181,80
%N A341979 Number of partitions of n into 8 distinct primes (counting 1 as a prime).
%p A341979 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A341979      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))(
%p A341979      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 9)
%p A341979     end:
%p A341979 a:= n-> coeff(b(n, numtheory[pi](n)), x, 8):
%p A341979 seq(a(n), n=59..130);  # _Alois P. Heinz_, Feb 24 2021
%t A341979 b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t A341979      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i - 1]]][
%t A341979      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 9}];
%t A341979 a[n_] := Coefficient[b[n, PrimePi[n]], x, 8];
%t A341979 Table[a[n], {n, 59, 130}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)
%Y A341979 Cf. A008578, A036497, A219202, A341951, A341973, A341974, A341975, A341976, A341977, A341978, A341980, A341981.
%K A341979 nonn
%O A341979 59,7
%A A341979 _Ilya Gutkovskiy_, Feb 24 2021