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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.)