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A325054
Sum of all compositions [c_1, c_2, ..., c_q] of n encoded as Product_{i=1..q} prime(i)^(c_i).
3
1, 2, 10, 68, 640, 8372, 147820, 3321908, 90184300, 2857153892, 104146026820, 4363900557128, 209763325978480, 11462371025215112, 702793156696129600, 47649412958404240688, 3521160558576929028400, 280427910532671712997732, 23932837097476310995036900
OFFSET
0,2
LINKS
EXAMPLE
The compositions of 3 and their encodings are [1,1,1]-> 30, [1,2]-> 18, [2,1]-> 12, [3]-> 8. The sum gives a(3) = 68.
MAPLE
b:= proc(n, j) option remember; `if`(n=0, 1,
add(ithprime(j)^i*b(n-i, j+1), i=1..n))
end:
a:= n-> b(n, 1):
seq(a(n), n=0..20); # Alois P. Heinz, Sep 04 2019
MATHEMATICA
b[n_, j_] := b[n, j] = If[n==0, 1, Sum[Prime[j]^i*b[n-i, j+1], {i, 1, n}]];
a[n_] := b[n, 1];
a /@ Range[0, 20] (* Jean-François Alcover, Apr 23 2021, after Alois P. Heinz *)
CROSSREFS
Row sums of A324939.
Sequence in context: A104098 A056755 A123617 * A139715 A293914 A259114
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 04 2019
STATUS
approved