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Search: id:A116688
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| A116688 |
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Sum over all partitions of n of the sum of the parts that are smaller than the largest part. |
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+0
2
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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a(n)=Sum(k*A116687(n,k),k>=0).
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FORMULA
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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 (vladeta(AT)Eunet.yu), Feb 24 2006
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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Cf. A116687.
Sequence in context: A006459 A049778 A123325 this_sequence A011755 A128301 A018307
Adjacent sequences: A116685 A116686 A116687 this_sequence A116689 A116690 A116691
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 23 2006
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