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A252782 a(n) = n-th term of Euler transform of n-th powers. 11
1, 1, 5, 36, 490, 12729, 689896, 70223666, 13803604854, 5567490203192, 4386006155453382, 6711625359213752077, 21048250447828058144403, 131214686495783317936950378, 1603891839732647136012816743764, 40296598014204065945778862754895836 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..80

Vaclav Kotesovec, Graph - The asymptotic ratio

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.

Cf. A008485, A073229, A255672, A270917.

Sequence in context: A241346 A132686 A322180 * A292194 A118018 A318424

Adjacent sequences:  A252779 A252780 A252781 * A252783 A252784 A252785

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 21 2014

STATUS

approved

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Last modified September 17 13:00 EDT 2019. Contains 327131 sequences. (Running on oeis4.)