OFFSET
0,3
COMMENTS
Also partitions of n into 1 sort of 1, 4 sorts of 2, 27 sorts of 3, ..., k^k sorts of k. - Joerg Arndt, Feb 04 2015
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
FORMULA
G.f.: 1 / Product_{k>=1} (1 - x^k)^(k^k).
a(n) ~ n^n * (1 + exp(-1)/n + (exp(-1)/2 + 5*exp(-2))/n^2). - Vaclav Kotesovec, Mar 14 2015
a(n) = (1/n)*Sum_{k=1..n} A283498(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 11 2017
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(
add(d*d^d, d=divisors(j)) *a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Feb 04 2015
MATHEMATICA
nmax=20; CoefficientList[Series[Product[1/(1-x^k)^(k^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)
PROG
(PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^(k^k))) \\ G. C. Greubel, Oct 31 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^(k^k): k in [1..m]]) )); // G. C. Greubel, Oct 31 2018
(SageMath) # uses[EulerTransform from A166861]
b = EulerTransform(lambda n: n^n)
print([b(n) for n in range(20)]) # Peter Luschny, Nov 11 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved