OFFSET
1,5
FORMULA
G.f.: Sum_{k>0} x^(2k-1)/(Product_{0<i<k} 1-x^(2i-1)).
a(n) = A000009(n-2), n>2. - Michael Somos, May 28 2006
a(n) = A117408(n,1).
a(n) ~ exp(Pi*sqrt(n/3)) / (4*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 27 2016
EXAMPLE
a(9)=5 because we have [9],[7,1,1],[5,3,1],[5,1,1,1,1] and [3,1,1,1,1,1,1].
MAPLE
f:=sum(x^(2*k-1)/product(1-x^(2*i-1), i=1..k-1), k=1..40): fser:=series(f, x=0, 70): seq(coeff(fser, x^n), n=1..65);
MATHEMATICA
Table[SeriesCoefficient[Sum[x^(2 k - 1)/Product[1 - x^(2 i - 1), {i, k - 1}], {k, 0, n}] , {x, 0, n}], {n, 57}] (* Michael De Vlieger, Sep 16 2016 *)
PROG
(PARI) {a(n)=if(n<3, n==1, n-=2; polcoeff( prod(k=1, n, 1+x^k, 1+x*O(x^n)), n))} /* Michael Somos, May 28 2006 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Mar 13 2006
STATUS
approved