This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259200 #48 Jun 19 2025 22:20:20
%S A259200 1,1,1,2,2,3,4,4,5,7,7,9,10,11,12,16,16,20,21,24,26,33,31,39,39,47,46,
%T A259200 59,53,69,65,80,77,98,85,114,104,131,118,154,133,179,155,200,177,236,
%U A259200 196,268,227,300,256
%N A259200 Number of partitions of n into nine primes.
%H A259200 Robert Israel, <a href="/A259200/b259200.txt">Table of n, a(n) for n = 18..10000</a>
%H A259200 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A259200 a(n) = [x^n y^9] Product_{k>=1} 1/(1 - y*x^prime(k)). - _Ilya Gutkovskiy_, Apr 18 2019
%F A259200 a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} c(q) * c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p-q), where c = A010051. - _Wesley Ivan Hurt_, Jul 13 2019
%e A259200 a(23) = 3 because there are 3 partitions of 23 into nine primes: [2,2,2,2,2,2,2,2,7], [2,2,2,2,2,2,3,3,5] and [2,2,2,2,3,3,3,3,3].
%p A259200 N:= 100: # to get a(0) to a(N)
%p A259200 Primes:= select(isprime,[$1..N]):
%p A259200 np:= nops(Primes):
%p A259200 for j from 0 to np do g[0,j]:= 1 od:
%p A259200 for n from 1 to 9 do
%p A259200 g[n,0]:= 0:
%p A259200 for j from 1 to np do
%p A259200 g[n,j]:= convert(series(add(g[k,j-1]
%p A259200 *x^((n-k)*Primes[j]),k=0..n),x,N+1),polynom)
%p A259200 od
%p A259200 od:
%p A259200 seq(coeff(g[9,np],x,i),i=18..N) # _Robert Israel_, Jun 21 2015
%t A259200 Table[Length[Select[IntegerPartitions[n],Length[#]==9&&AllTrue[ #, PrimeQ]&]], {n,18,70}] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 31 2016 *)
%o A259200 (PARI) a(n) = {nb = 0; forpart(p=n, if (#p && (#select(x->isprime(x), Vec(p)) == #p), nb+=1), , [9,9]); nb;} \\ _Michel Marcus_, Jun 21 2015
%o A259200 (Magma) [#RestrictedPartitions(k,9,Set(PrimesUpTo(1000))):k in [18..70]] ; // _Marius A. Burtea_, Jul 13 2019
%Y A259200 Column k=9 of A117278.
%Y A259200 Number of partitions of n into r primes for r = 1..10: A010051, A061358, A068307, A259194, A259195, A259196, A259197, A259198, this sequence, A259201.
%Y A259200 Cf. A000040.
%K A259200 nonn,easy
%O A259200 18,4
%A A259200 _Doug Bell_, Jun 20 2015