cp's OEIS Frontend

A117409 Number of partitions of n into odd parts in which the largest part occurs only once.

%I A117409 #25 Sep 27 2016 13:48:05
%S A117409 1,0,1,1,2,2,3,4,5,6,8,10,12,15,18,22,27,32,38,46,54,64,76,89,104,122,
%T A117409 142,165,192,222,256,296,340,390,448,512,585,668,760,864,982,1113,
%U A117409 1260,1426,1610,1816,2048,2304,2590,2910,3264,3658,4097,4582,5120,5718,6378
%N A117409 Number of partitions of n into odd parts in which the largest part occurs only once.
%F A117409 G.f.: Sum_{k>0} x^(2k-1)/(Product_{0<i<k} 1-x^(2i-1)).
%F A117409 a(n) = A000009(n-2), n>2. - _Michael Somos_, May 28 2006
%F A117409 a(n) = A117408(n,1).
%F A117409 a(n) ~ exp(Pi*sqrt(n/3)) / (4*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Sep 27 2016
%e A117409 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].
%p A117409 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);
%t A117409 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 *)
%o A117409 (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 */
%Y A117409 Cf. A117408.
%K A117409 nonn
%O A117409 1,5
%A A117409 _Emeric Deutsch_, Mar 13 2006