cp's OEIS Frontend

A341984 Number of ways to write n as an ordered sum of 5 primes (counting 1 as a prime).

%I A341984 #5 Feb 24 2021 21:47:35
%S A341984 1,5,15,30,50,71,100,130,170,195,231,250,310,340,420,430,525,535,685,
%T A341984 680,851,800,1025,970,1280,1145,1470,1250,1685,1440,1991,1600,2230,
%U A341984 1790,2615,2070,2985,2190,3250,2410,3700,2665,4125,2840,4560,3200,5135,3470,5670,3705,6226,4120
%N A341984 Number of ways to write n as an ordered sum of 5 primes (counting 1 as a prime).
%F A341984 G.f.: ( x + Sum_{k>=1} x^prime(k) )^5.
%p A341984 b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
%p A341984       `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 6)
%p A341984     end:
%p A341984 a:= n-> coeff(b(n), x, 5):
%p A341984 seq(a(n), n=5..56);  # _Alois P. Heinz_, Feb 24 2021
%t A341984 nmax = 56; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341984 Cf. A008578, A280917, A283762, A340961, A341948, A341976, A341982, A341983.
%K A341984 nonn
%O A341984 5,2
%A A341984 _Ilya Gutkovskiy_, Feb 24 2021