OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..380
FORMULA
Log of g.f.: Sum_{k>=1} (sigma(k, k+1)/k) x^k, where sigma(k, q) is the sum of the q-th powers of the divisors of k.
a(n) ~ n^n * (1 + exp(-1)/n + (1/2*exp(-1)+5*exp(-2))/n^2). - Vaclav Kotesovec, Dec 19 2015
a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A294645(k)*a(n-k) for n > 0. - Seiichi Manyama, Nov 09 2017
MAPLE
seq(coeff(series(1/mul(1-k^k*x^k, k=1..n), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 31 2018
MATHEMATICA
nmax=20; CoefficientList[Series[Product[1/(1-k^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 19 2015 *)
PROG
(PARI) m=20; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-k^k*x^k))) \\ G. C. Greubel, Oct 30 2018
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-k^k*x^k): k in [1..m]]) )); // G. C. Greubel, Oct 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved