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A341986
Number of ways to write n as an ordered sum of 7 primes (counting 1 as a prime).
5
1, 7, 28, 77, 168, 308, 511, 785, 1155, 1603, 2142, 2723, 3430, 4207, 5202, 6216, 7497, 8729, 10451, 12061, 14350, 16205, 19033, 21182, 24934, 27482, 32109, 34587, 40139, 42714, 49791, 52290, 60718, 62699, 73297, 75278, 88571, 89488, 104993, 104482, 123760, 122066
OFFSET
7,2
LINKS
FORMULA
G.f.: ( x + Sum_{k>=1} x^prime(k) )^7.
MAPLE
b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
`if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 8)
end:
a:= n-> coeff(b(n), x, 7):
seq(a(n), n=7..48); # Alois P. Heinz, Feb 25 2021
MATHEMATICA
nmax = 48; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 24 2021
STATUS
approved