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

1,5

Links

Table of n, a(n) for n=1..57.

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

Cf. A117408.

Sequence in context: A347588 A000009 A081360 * A092833 A280664 A100926

Adjacent sequences: A117406 A117407 A117408 * A117410 A117411 A117412

Keyword

nonn

Author

Emeric Deutsch, Mar 13 2006

Status

approved