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A252782
a(n) = n-th term of Euler transform of n-th powers.
12
1, 1, 5, 36, 490, 12729, 689896, 70223666, 13803604854, 5567490203192, 4386006155453382, 6711625359213752077, 21048250447828058144403, 131214686495783317936950378, 1603891839732647136012816743764, 40296598014204065945778862754895836
OFFSET
0,3
LINKS
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
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 *)
CROSSREFS
Main diagonal of A144048.
Sequence in context: A132686 A322180 A351019 * A292194 A118018 A318424
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 21 2014
STATUS
approved