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A341977 Number of partitions of n into 6 distinct primes (counting 1 as a prime).

%I A341977 #14 Mar 06 2021 10:18:14
%S A341977 1,0,1,0,0,0,2,0,2,0,2,1,5,0,4,1,5,2,8,1,7,2,8,4,12,2,12,6,14,7,17,5,
%T A341977 18,8,20,11,26,10,27,15,30,18,36,17,36,22,41,28,48,25,49,35,56,40,61,
%U A341977 38,64,50,73,56,77,54,82,70,93,74,96,78,106,92,114,100
%N A341977 Number of partitions of n into 6 distinct primes (counting 1 as a prime).
%H A341977 Alois P. Heinz, <a href="/A341977/b341977.txt">Table of n, a(n) for n = 29..10000</a>
%p A341977 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A341977      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))(
%p A341977      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 7)
%p A341977     end:
%p A341977 a:= n-> coeff(b(n, numtheory[pi](n)), x, 6):
%p A341977 seq(a(n), n=29..100);  # _Alois P. Heinz_, Feb 24 2021
%t A341977 m = 6;
%t A341977 b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t A341977      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i - 1]]][
%t A341977      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, m + 1}];
%t A341977 a[n_] :=  Coefficient[b[n, PrimePi[n]], x, m];
%t A341977 Table[a[n], {n, 29, 100}] (* _Jean-François Alcover_, Mar 06 2021, after _Alois P. Heinz_ *)
%Y A341977 Cf. A008578, A036497, A219200, A341949, A341973, A341974, A341975, A341976.
%K A341977 nonn
%O A341977 29,7
%A A341977 _Ilya Gutkovskiy_, Feb 24 2021