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A341989
Number of ways to write n as an ordered sum of 10 primes (counting 1 as a prime).
4
1, 10, 55, 210, 625, 1542, 3310, 6390, 11400, 19090, 30353, 46060, 67210, 94780, 130230, 174862, 230650, 298800, 382115, 482090, 603373, 746860, 918770, 1118100, 1355110, 1626742, 1949190, 2312380, 2740220, 3212640, 3769784, 4375900, 5092485, 5854680, 6758935, 7703112
OFFSET
10,2
FORMULA
G.f.: ( x + Sum_{k>=1} x^prime(k) )^10.
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, 11)
end:
a:= n-> coeff(b(n), x, 10):
seq(a(n), n=10..45); # Alois P. Heinz, Feb 25 2021
MATHEMATICA
nmax = 45; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 24 2021
STATUS
approved