OFFSET
1,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
G.f. for total number of parts of multiplicity m in all partitions of n is (x^m/(1-x^m)-x^(m+1)/(1-x^(m+1)))/Product(1-x^i,i=1..infinity).
a(n) = Sum(k*A118806(n,k), k>=0). - Emeric Deutsch, Apr 29 2006
a(n) ~ exp(Pi*sqrt(2*n/3)) / (24*Pi*sqrt(2*n)). - Vaclav Kotesovec, May 24 2018
EXAMPLE
a(9) = 7 because among the 30 (=A000041(9)) partitions of 9 only [6,(1,1,1)],[4,2,(1,1,1)],[(3,3,3)],[3,3,(1,1,1)],[3,(2,2,2)],[(2,2,2),(1,1,1)] contain parts of multiplicity 3 and their total number is 7 (shown between parentheses)
MAPLE
g:=(x^3/(1-x^3)-x^4/(1-x^4))/product(1-x^i, i=1..65): gser:=series(g, x=0, 62): seq(coeff(gser, x, n), n=1..58); # Emeric Deutsch, Apr 29 2006
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 26 2006
STATUS
approved