OFFSET
1,3
COMMENTS
a(n) = Sum_{k>=1} k*A116856(n,k). - Emeric Deutsch, Feb 24 2006
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..2500
FORMULA
G.f.: Sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k = n .. infinity), n = 1 .. infinity).
a(n) ~ exp(Pi*sqrt(n/3)) / (4 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 07 2019
EXAMPLE
a(5)=7 because the partitions of 5 into odd parts are [5],[3,1,1] and [1,1,1,1,1] and the smallest parts add up to 5+1+1=7.
MAPLE
g:=sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k=n..30), n=1..30): gser:=series(g, x=0, 57): seq(coeff(gser, x^n), n=1..54); # Emeric Deutsch, Feb 24 2006
MATHEMATICA
nmax = 50; Rest[CoefficientList[Series[Sum[(2*n - 1)*x^(2*n - 1) / Product[(1 - x^(2*k - 1)), {k, n, nmax}], {n, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 06 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 15 2004
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
STATUS
approved