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A219201
Number of partitions of n into 7 distinct primes.
5
1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 4, 0, 3, 0, 3, 1, 6, 0, 6, 1, 5, 1, 10, 0, 11, 2, 9, 3, 16, 1, 17, 3, 15, 5, 25, 4, 24, 5, 25, 10, 35, 6, 34, 10, 36, 15, 48, 10, 50, 17, 52, 23, 65, 17, 69, 27, 70, 32, 89, 30, 93, 38, 93, 48, 116, 43, 121, 56, 125, 70, 148
OFFSET
58,7
LINKS
FORMULA
G.f.: Sum_{0<i_1<i_2<...<i_7} x^(Sum_{j=1..7} prime(i_j)).
a(n) = [x^n*y^7] Product_{i>=1} (1+x^prime(i)*y).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0$7], `if`(i<1, [0$8],
zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$7],
b(n-ithprime(i), i-1)[1..7])[]], 0)))
end:
a:= n-> b(n, numtheory[pi](n))[8]:
seq(a(n), n=58..140);
MATHEMATICA
k = 7; b[n_, i_] := b[n, i] = If[n == 0, Join[{1}, Array[0&, k]], If[i<1, Array[0&, k+1], Plus @@ PadRight[{b[n, i-1], Join[{0}, If[Prime[i]>n, Array[0&, k], Take[b[n-Prime[i], i-1], k]]]}]]]; a[n_] := b[n, PrimePi[n]][[k+1]]; Table[a[n], {n, 58, 140}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *)
CROSSREFS
Column k=7 of A219180.
Sequence in context: A159200 A338021 A318721 * A341979 A331838 A361017
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 14 2012
STATUS
approved