[go: up one dir, main page]

login
A117409
Number of partitions of n into odd parts in which the largest part occurs only once.
26
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
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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Mar 13 2006
STATUS
approved