OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..400
FORMULA
a(n) = coefficient of x^n*y^n/(2*n) in Sum_{n>=1} -log(1 - (x^n + y^n)) for n>=0.
a(n) ~ 4^n / sqrt(Pi*n). - Vaclav Kotesovec, Jun 18 2019
EXAMPLE
L.g.f.: L(x) = 2*x + 10*x^2/2 + 26*x^3/3 + 90*x^4/4 + 262*x^5/5 + 994*x^6/6 + 3446*x^7/7 + 13050*x^8/8 + 48698*x^9/9 + 185310*x^10/10 + 705454*x^11/11 + 2706354*x^12/12 + ...
such that
exp( L(x) ) = 1 + 2*x + 7*x^2 + 20*x^3 + 63*x^4 + 190*x^5 + 613*x^6 + 1976*x^7 + 6604*x^8 + 22368*x^9 + 77270*x^10 + 270208*x^11 + 956780*x^12 + ...
PROG
(PARI)
{L = sum(n=1, 61, -log(1 - (x^n + y^n) +O(x^61) +O(y^61)) ); }
{a(n) = polcoeff( 2*n*polcoeff( L, n, x), n, y)}
for(n=0, 35, print1( a(n), ", ") )
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 30 2018
STATUS
approved