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%I #8 Feb 24 2022 09:58:48
%S 1,0,0,0,0,0,1,0,1,0,1,0,2,0,2,0,1,0,5,0,4,0,2,0,9,0,7,1,7,1,14,0,10,
%T 0,12,2,22,0,19,2,22,3,34,1,31,4,32,5,54,3,48,7,50,9,78,7,70,11,76,16,
%U 113,9,100,19,114,26,155,17,147,32,164,37,212,26
%N Number of partitions of n into 10 distinct primes (counting 1 as a prime).
%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-1)))(
%p `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 11)
%p end:
%p a:= n-> coeff(b(n, numtheory[pi](n)), x, 10):
%p seq(a(n), n=101..174); # _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 - 1]]][
%t If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 11}];
%t a[n_] := Coefficient[b[n, PrimePi[n]], x, 10];
%t Table[a[n], {n, 101, 174}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)
%Y Cf. A008578, A036497, A219204, A341972, A341973, A341974, A341975, A341976, A341977, A341978, A341979, A341980.
%K nonn
%O 101,13
%A _Ilya Gutkovskiy_, Feb 24 2021
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