A325054 Sum of all compositions [c_1, c_2, ..., c_q] of n encoded as Product_{i=1..q} prime(i)^(c_i).

1, 2, 10, 68, 640, 8372, 147820, 3321908, 90184300, 2857153892, 104146026820, 4363900557128, 209763325978480, 11462371025215112, 702793156696129600, 47649412958404240688, 3521160558576929028400, 280427910532671712997732, 23932837097476310995036900

Offset: 0

Author

Alois P. Heinz, Sep 04 2019

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..335
• Wikipedia, Gödel's encoding

Crossrefs

Row sums of A324939.

Cf. A000040, A074140.

Programs

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 *)