%I #5 Feb 25 2021 08:32:50

%S 1,8,36,112,274,560,1016,1688,2647,3928,5580,7568,9990,12832,16332,

%T 20336,25167,30472,37004,44136,53054,62272,73788,85240,100276,114752,

%U 134072,151144,174834,194616,224304,247240,283467,308448,352668,381032,436368,467272,533520

%N Number of ways to write n as an ordered sum of 8 primes (counting 1 as a prime).

%F G.f.: ( x + Sum_{k>=1} x^prime(k) )^8.

%t nmax = 46; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &

%Y Cf. A008578, A280917, A283762, A340964, A341951, A341979, A341982, A341983, A341984, A341985, A341986, A341988, A341989.

%K nonn

%O 8,2

%A _Ilya Gutkovskiy_, Feb 24 2021