OFFSET
0,3
FORMULA
G.f.: (1-x^8) Product_{m>0} 1/(1-x^m).
a(n) ~ 2*Pi * exp(sqrt(2*n/3)*Pi) / (3*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 8*Pi/(2*sqrt(6)))/sqrt(n) + (97/8 + 9/(2*Pi^2) + 12481*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016
MATHEMATICA
Table[Count[IntegerPartitions[n], _?(FreeQ[#, 8]&)], {n, 0, 50}] (* Harvey P. Dale, Mar 11 2017 *)
PROG
(PARI) a(n)=if(n<0, 0, polcoeff((1-x^8)/eta(x+x*O(x^n)), n))
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Benoit Cloitre, Dec 10 2002
STATUS
approved