OFFSET
1,4
COMMENTS
a(n) = Sum(k*A116685(n,k), k>=0).
Also, sum over all partitions of n of the difference between the largest part and the smallest part. - Franklin T. Adams-Watters, Feb 29 2008
Row sums of A244966. - Omar E. Pol, Jul 19 2014
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: sum[x^i*sum(x^j/(1-x^j),j=1..i-1)/product(1-x^q, q=1..i)], i=1..infinity).
EXAMPLE
a(5) = 8 because the partitions of 5 are [5], [4,(1)], [3,(2)], [3,(1),(1)], [2,2,(1)], [2,(1),(1),(1)] and [1,1,1,1,1], containing a total of 8 parts that are smaller than the largest part (shown between parentheses).
MAPLE
f:=sum(x^i*sum(x^j/(1-x^j), j=1..i-1)/product(1-x^q, q=1..i), i=2..55): fser:=series(f, x=0, 50): seq(coeff(fser, x^n), n=1..47);
MATHEMATICA
Table[Length[Flatten[Rest[Split[#]]&/@Select[IntegerPartitions[n], #[[1]]> #[[-1]]&]]], {n, 50}] (* Harvey P. Dale, Jul 26 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 23 2006
STATUS
approved