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A117525
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Total sum of parts of multiplicity 2 in all partitions of n.
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0
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0, 1, 0, 3, 3, 7, 9, 20, 22, 44, 56, 90, 119, 186, 236, 355, 461, 651, 848, 1177, 1506, 2050, 2626, 3482, 4443, 5823, 7353, 9524, 11983, 15307, 19163, 24277, 30174, 37920, 46925, 58463, 72006, 89155, 109209, 134418, 163973, 200605, 243700, 296696
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| G.f. for total sum of parts of multiplicity m in all partitions of n is (x^m/(1-x^m)^2-x^(m+1)/(1-x^(m+1))^2)/Product(1-x^i,i=1..infinity).
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EXAMPLE
| a(5)=3 because the partitions of 5 that have parts with multiplicity 2 are [3,1,1] and [2,2,1] and the sum of those parts is 1+2=3.
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MAPLE
| g:=(x^2/(1-x^2)^2-x^3/(1-x^3)^2)/Product(1-x^i, i=1..60): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=1..50); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2006
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CROSSREFS
| Cf. A103628.
Sequence in context: A048240 A122012 A056295 * A075149 A161618 A202873
Adjacent sequences: A117522 A117523 A117524 * A117526 A117527 A117528
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 26 2006
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2006
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