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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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1
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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
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OFFSET
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1,4
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COMMENTS
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LINKS
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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).
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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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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