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A340964 Number of ways to write n as an ordered sum of 8 primes.

%I A340964 #10 Mar 18 2022 18:39:22
%S A340964 1,8,28,64,126,232,392,624,925,1296,1800,2416,3158,4088,5152,6504,
%T A340964 8142,9976,12216,14784,17738,21296,25272,29736,35023,40768,47328,
%U A340964 54832,62728,71744,81796,92736,105078,118664,132924,149424,167002,186144,206852,229272,253023
%N A340964 Number of ways to write n as an ordered sum of 8 primes.
%H A340964 Seiichi Manyama, <a href="/A340964/b340964.txt">Table of n, a(n) for n = 16..10000</a>
%F A340964 G.f.: (Sum_{k>=1} x^prime(k))^8.
%p A340964 b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
%p A340964       if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
%p A340964       while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
%p A340964     end:
%p A340964 a:= n-> b(n, 8):
%p A340964 seq(a(n), n=16..56);  # _Alois P. Heinz_, Jan 31 2021
%t A340964 nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 16] &
%Y A340964 Column k=8 of A121303.
%Y A340964 Cf. A000040, A010051, A073610, A098238, A259198, A340960, A340961, A340962, A340963, A340965, A340966.
%K A340964 nonn
%O A340964 16,2
%A A340964 _Ilya Gutkovskiy_, Jan 31 2021