OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..370
FORMULA
G.f.: exp( Sum_{k>0} sigma_k(k) * x^k / k). - Michael Somos, Feb 15 2006
G.f.: Product_{n>=1} (1 - n^n*x^n)^(-1/n). - Paul D. Hanna, Mar 08 2011
a(n) ~ n^(n-1). - Vaclav Kotesovec, Oct 08 2016
EXAMPLE
G.f. = 1 + x + 3*x^2 + 12*x^3 + 82*x^4 + 725*x^5 + 8811*x^6 + 128340*x^7 + 2257687*x^8 + ...
MAPLE
seq(coeff(series(mul((1-k^k*x^k)^(-1/k), k=1..n), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 31 2018
MATHEMATICA
nmax=30; CoefficientList[Series[Product[1/(1-k^k*x^k)^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] (* G. C. Greubel, Oct 31 2018 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( exp( sum( k=1, n, sigma(k, k) * x^k / k, x * O(x^n))), n))} /* Michael Somos, Feb 15 2006 */
(PARI) {a(n)=if(n<0, 0, polcoeff(prod(k=1, n, (1-k^k*x^k+x*O(x^n))^(-1/k)), n))} /* Paul D. Hanna */
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-k^k*x^k)^(1/k): k in [1..m]]) )); // G. C. Greubel, Oct 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved