A341980 - OEIS

%I #9 Feb 24 2022 09:58:31

%S 1,0,0,0,1,0,1,0,0,0,2,0,3,0,1,0,3,0,5,0,4,1,6,0,10,0,6,1,11,1,16,1,

%T 11,2,19,2,25,1,18,5,32,4,36,2,32,9,47,7,55,7,49,14,69,10,80,12,74,22,

%U 98,19,117,22,106,34,140,31,158,32,149,54,194,48,215,50

%N Number of partitions of n into 9 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, 10)

%p     end:

%p a:= n-> coeff(b(n, numtheory[pi](n)), x, 9):

%p seq(a(n), n=78..151);  # _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, 10}];

%t a[n_] := Coefficient[b[n, PrimePi[n]], x, 9];

%t Table[a[n], {n, 78, 151}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)

%Y Cf. A008578, A036497, A219203, A341719, A341973, A341974, A341975, A341976, A341977, A341978, A341979, A341981.

%K nonn

%O 78,11

%A _Ilya Gutkovskiy_, Feb 24 2021