A252782 a(n) = n-th term of Euler transform of n-th powers.

1, 1, 5, 36, 490, 12729, 689896, 70223666, 13803604854, 5567490203192, 4386006155453382, 6711625359213752077, 21048250447828058144403, 131214686495783317936950378, 1603891839732647136012816743764, 40296598014204065945778862754895836

Offset: 0

Author

Alois P. Heinz, Dec 21 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..80
• Vaclav Kotesovec, Graph - The asymptotic ratio

Crossrefs

Main diagonal of A144048.

Cf. A008485, A073229, A255672, A270917.

Programs

Maple

with(numtheory):
A:= proc(n, k) option remember; `if`(n=0, 1, add(add(
       d*d^k, d=divisors(j))*A(n-j, k), j=1..n)/n)
    end:
a:= n-> A(n$2):
seq(a(n), n=0..20);

Mathematica

Table[SeriesCoefficient[Product[1/(1-x^k)^(k^n),{k,1,n}],{x,0,n}], {n,0,20}] (* Vaclav Kotesovec, Mar 01 2015 *)

Formula

a(n) = [x^n] Product_{j>=1} 1/(1-x^j)^(j^n).

Conjecture: limit n->infinity a(n)^(1/n^2) = exp(exp(-1)) = 1.444667861... . - Vaclav Kotesovec, Mar 25 2016