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A341951 Number of partitions of n into 8 primes (counting 1 as a prime).

%I A341951 #10 Feb 15 2022 08:15:44
%S A341951 1,1,2,2,4,4,7,7,11,10,15,14,21,19,27,23,35,30,44,37,54,44,67,55,81,
%T A341951 65,96,75,115,89,133,102,155,116,180,134,206,153,236,171,271,194,305,
%U A341951 220,346,242,391,273,438,305,489,334,551,374,608,412,674,447,750,494,823
%N A341951 Number of partitions of n into 8 primes (counting 1 as a prime).
%p A341951 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A341951      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
%p A341951      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 9)
%p A341951     end:
%p A341951 a:= n-> coeff(b(n, numtheory[pi](n)), x, 8):
%p A341951 seq(a(n), n=8..68);  # _Alois P. Heinz_, Feb 24 2021
%t A341951 b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t A341951      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
%t A341951      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 9}];
%t A341951 a[n_] := Coefficient[b[n, PrimePi[n]], x, 8];
%t A341951 Table[a[n], {n, 8, 68}] (* _Jean-François Alcover_, Feb 15 2022, after _Alois P. Heinz_ *)
%Y A341951 Cf. A008578, A034891, A259198, A341945, A341946, A341947, A341948, A341949, A341950.
%K A341951 nonn
%O A341951 8,3
%A A341951 _Ilya Gutkovskiy_, Feb 24 2021