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A340965 Number of ways to write n as an ordered sum of 9 primes.

%I A340965 #10 Mar 18 2022 18:39:53
%S A340965 1,9,36,93,198,387,696,1170,1845,2740,3960,5562,7566,10125,13248,
%T A340965 17133,22014,27774,34776,43173,53010,64869,78696,94617,113415,134946,
%U A340965 159552,188164,219960,256041,297180,342846,394614,452595,516276,587997,667938,755109,852444
%N A340965 Number of ways to write n as an ordered sum of 9 primes.
%H A340965 Seiichi Manyama, <a href="/A340965/b340965.txt">Table of n, a(n) for n = 18..10000</a>
%F A340965 G.f.: (Sum_{k>=1} x^prime(k))^9.
%p A340965 b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
%p A340965       if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
%p A340965       while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
%p A340965     end:
%p A340965 a:= n-> b(n, 9):
%p A340965 seq(a(n), n=18..56);  # _Alois P. Heinz_, Jan 31 2021
%t A340965 nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 18] &
%Y A340965 Column k=9 of A121303.
%Y A340965 Cf. A000040, A010051, A073610, A098238, A259200, A340960, A340961, A340962, A340963, A340964, A340966.
%K A340965 nonn
%O A340965 18,2
%A A340965 _Ilya Gutkovskiy_, Jan 31 2021