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A341950
Number of partitions of n into 7 primes (counting 1 as a prime).
11
1, 1, 2, 2, 4, 4, 7, 7, 10, 9, 14, 12, 19, 16, 23, 19, 30, 24, 37, 29, 44, 35, 55, 41, 65, 49, 75, 56, 89, 63, 102, 72, 116, 82, 134, 91, 153, 105, 171, 115, 194, 128, 220, 143, 242, 158, 273, 174, 305, 193, 334, 211, 374, 231, 412, 250, 447, 273, 494, 294, 541, 321
OFFSET
7,3
LINKS
MAPLE
b:= proc(n, i) option remember; series(`if`(n=0, 1,
`if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
`if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 8)
end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 7):
seq(a(n), n=7..68); # Alois P. Heinz, Feb 24 2021
MATHEMATICA
b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 8}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 7];
Table[a[n], {n, 7, 68}] (* Jean-François Alcover, Feb 15 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 24 2021
STATUS
approved