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%I #5 Feb 25 2021 08:32:56
%S 1,9,45,156,423,954,1887,3384,5661,8935,13446,19332,26838,36126,47691,
%T 61668,78696,98631,122665,150516,184230,222438,268146,318564,379383,
%U 445572,525942,610344,712872,817290,947166,1075680,1238148,1391475,1591236,1773684,2022241
%N Number of ways to write n as an ordered sum of 9 primes (counting 1 as a prime).
%F G.f.: ( x + Sum_{k>=1} x^prime(k) )^9.
%t nmax = 45; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^9, {x, 0, nmax}], x] // Drop[#, 9] &
%Y Cf. A008578, A280917, A283762, A340965, A341719, A341980, A341982, A341983, A341984, A341985, A341986, A341987, A341989.
%K nonn
%O 9,2
%A _Ilya Gutkovskiy_, Feb 24 2021