A117409 Number of partitions of n into odd parts in which the largest part occurs only once.
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, 142, 165, 192, 222, 256, 296, 340, 390, 448, 512, 585, 668, 760, 864, 982, 1113, 1260, 1426, 1610, 1816, 2048, 2304, 2590, 2910, 3264, 3658, 4097, 4582, 5120, 5718, 6378
Offset: 1
Keywords
Examples
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].
Crossrefs
Cf. A117408.
Programs
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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);
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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 *) -
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 */
Formula
G.f.: Sum_{k>0} x^(2k-1)/(Product_{0
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