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%I #13 Feb 15 2022 08:15:48
%S 1,1,2,2,4,4,7,7,10,9,14,12,19,16,23,19,30,24,37,29,44,35,55,41,65,49,
%T 75,56,89,63,102,72,116,82,134,91,153,105,171,115,194,128,220,143,242,
%U 158,273,174,305,193,334,211,374,231,412,250,447,273,494,294,541,321
%N Number of partitions of n into 7 primes (counting 1 as a prime).
%H Alois P. Heinz, <a href="/A341950/b341950.txt">Table of n, a(n) for n = 7..10000</a>
%p b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
%p `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 8)
%p end:
%p a:= n-> coeff(b(n, numtheory[pi](n)), x, 7):
%p seq(a(n), n=7..68); # _Alois P. Heinz_, Feb 24 2021
%t b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
%t If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 8}];
%t a[n_] := Coefficient[b[n, PrimePi[n]], x, 7];
%t Table[a[n], {n, 7, 68}] (* _Jean-François Alcover_, Feb 15 2022, after _Alois P. Heinz_ *)
%Y Cf. A008578, A034891, A259197, A341945, A341946, A341947, A341948, A341949, A341951.
%K nonn
%O 7,3
%A _Ilya Gutkovskiy_, Feb 24 2021
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