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A340966 Number of ways to write n as an ordered sum of 10 primes.

%I A340966 #9 Mar 18 2022 18:39:38
%S A340966 1,10,45,130,300,622,1185,2100,3495,5480,8266,12100,17140,23730,32155,
%T A340966 42802,56400,73180,93820,119250,149872,187090,231765,284490,347335,
%U A340966 421332,507580,608840,725500,859450,1014473,1190700,1392100,1621710,1879950,2172610,2503580
%N A340966 Number of ways to write n as an ordered sum of 10 primes.
%H A340966 Seiichi Manyama, <a href="/A340966/b340966.txt">Table of n, a(n) for n = 20..10000</a>
%F A340966 G.f.: (Sum_{k>=1} x^prime(k))^10.
%p A340966 b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
%p A340966       if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
%p A340966       while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
%p A340966     end:
%p A340966 a:= n-> b(n, 10):
%p A340966 seq(a(n), n=20..56);  # _Alois P. Heinz_, Jan 31 2021
%t A340966 nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 20] &
%Y A340966 Column k=10 of A121303.
%Y A340966 Cf. A000040, A010051, A073610, A098238, A259201, A340960, A340961, A340962, A340963, A340964, A340965.
%K A340966 nonn
%O A340966 20,2
%A A340966 _Ilya Gutkovskiy_, Jan 31 2021