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A116688 Sum over all partitions of n of the sum of the parts that are smaller than the largest part. 1
0, 0, 1, 3, 9, 17, 36, 61, 106, 171, 273, 411, 627, 916, 1326, 1890, 2667, 3698, 5102, 6943, 9388, 12588, 16747, 22113, 29051, 37914, 49191, 63515, 81589, 104315, 132799, 168351, 212540, 267395, 335085, 418574, 521093, 646763, 800164, 987315 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n)=Sum(k*A116687(n,k),k>=0).

LINKS

Table of n, a(n) for n=1..40.

FORMULA

G.f.=sum(x^i*sum(jx^j/(1-x^j), j=1..i-1)/product(1-x^q, q=1..i), i=1..infinity).

a(n) = n*A000041(n) - A092321(n). - Vladeta Jovovic, Feb 24 2006

EXAMPLE

a(5)=9 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] and the sum of the parts (shown between parentheses) that are smaller than the largest part is 1+2+1+1+1+1+1+1=9.

MAPLE

f:=sum(x^i*sum(j*x^j/(1-x^j), j=1..i-1)/product(1-x^q, q=1..i), i=1..55): fser:=series(f, x=0, 50): seq(coeff(fser, x^n), n=1..47);

CROSSREFS

Cf. A116687.

Sequence in context: A294425 A123325 A239206 * A293423 A011755 A262466

Adjacent sequences:  A116685 A116686 A116687 * A116689 A116690 A116691

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 23 2006

STATUS

approved

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Last modified January 22 19:45 EST 2022. Contains 350504 sequences. (Running on oeis4.)