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%I #5 Feb 25 2021 08:32:38
%S 1,6,21,50,96,156,237,336,465,596,747,882,1077,1260,1536,1736,2067,
%T 2286,2761,3030,3627,3842,4578,4806,5826,6000,7167,7116,8562,8430,
%U 10318,9906,12093,11396,14286,13386,16868,15270,19242,17180,22218,19536,25393,21750,28680,24456
%N Number of ways to write n as an ordered sum of 6 primes (counting 1 as a prime).
%F G.f.: ( x + Sum_{k>=1} x^prime(k) )^6.
%t nmax = 51; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &
%Y Cf. A008578, A280917, A283762, A340962, A341949, A341977, A341982, A341983, A341984, A341986, A341987, A341988, A341989.
%K nonn
%O 6,2
%A _Ilya Gutkovskiy_, Feb 24 2021