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A341972 Number of partitions of n into 10 primes (counting 1 as a prime).

%I A341972 #14 Jun 01 2022 01:51:30
%S A341972 1,1,2,2,4,4,7,7,11,11,17,16,24,23,32,30,43,39,56,51,71,63,89,78,111,
%T A341972 97,134,116,164,139,197,166,232,194,275,227,324,265,374,305,438,351,
%U A341972 505,403,578,460,665,522,760,592,859,668,978,751,1105,844,1239,942,1394
%N A341972 Number of partitions of n into 10 primes (counting 1 as a prime).
%p A341972 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A341972      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
%p A341972      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 11)
%p A341972     end:
%p A341972 a:= n-> coeff(b(n, numtheory[pi](n)), x, 10):
%p A341972 seq(a(n), n=10..68);  # _Alois P. Heinz_, Feb 24 2021
%t A341972 b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t A341972      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
%t A341972      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 11}];
%t A341972 a[n_] := Coefficient[b[n, PrimePi[n]], x, 10];
%t A341972 Table[a[n], {n, 10, 68}] (* _Jean-François Alcover_, Feb 26 2022, after _Alois P. Heinz_ *)
%Y A341972 Cf. A008578, A034891, A259201, A341719, A341945, A341946, A341947, A341948, A341949, A341950, A341951.
%K A341972 nonn
%O A341972 10,3
%A A341972 _Ilya Gutkovskiy_, Feb 24 2021