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%I #8 Feb 25 2021 15:23:48
%S 1,7,28,77,168,308,511,785,1155,1603,2142,2723,3430,4207,5202,6216,
%T 7497,8729,10451,12061,14350,16205,19033,21182,24934,27482,32109,
%U 34587,40139,42714,49791,52290,60718,62699,73297,75278,88571,89488,104993,104482,123760,122066
%N Number of ways to write n as an ordered sum of 7 primes (counting 1 as a prime).
%H Alois P. Heinz, <a href="/A341986/b341986.txt">Table of n, a(n) for n = 7..10000</a>
%F G.f.: ( x + Sum_{k>=1} x^prime(k) )^7.
%p b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
%p `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 8)
%p end:
%p a:= n-> coeff(b(n), x, 7):
%p seq(a(n), n=7..48); # _Alois P. Heinz_, Feb 25 2021
%t nmax = 48; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &
%Y Cf. A008578, A280917, A283762, A340963, A341950, A341978, A341982, A341983, A341984, A341985, A341987, A341988, A341989.
%K nonn
%O 7,2
%A _Ilya Gutkovskiy_, Feb 24 2021