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A220486
a(n) = n(p(n)-d(n)): sum of all of parts of all partitions of n with at least one distinct part.
0
0, 0, 3, 8, 25, 42, 91, 144, 243, 380, 594, 852, 1287, 1834, 2580, 3616, 5015, 6822, 9272, 12420, 16548, 21956, 28819, 37608, 48875, 63232, 81162, 103936, 132327, 167880, 212040, 266976, 334587, 418404, 520765, 646848, 800495, 988418, 1216059, 1493200
OFFSET
1,3
FORMULA
a(n) = n*(A000041(n) - A000005(n)) = A066186(n) - A038040(n) = n*A144300(n).
EXAMPLE
For n = 6
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Partitions of 6 Value
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6 .......................... 0 (all parts are equal)
5 + 1 ...................... 6
4 + 2 ...................... 6
4 + 1 + 1 .................. 6
3 + 3 ...................... 0 (all parts are equal)
3 + 2 + 1 .................. 6
3 + 1 + 1 + 1 .............. 6
2 + 2 + 2 .................. 0 (all parts are equal)
2 + 2 + 1 + 1 .............. 6
2 + 1 + 1 + 1 + 1 .......... 6
1 + 1 + 1 + 1 + 1 + 1 ...... 0 (all parts are equal)
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The sum of the values is 42
On the other hand p(6) = A000041(6) = 11 and d(6) = A000005(6) = 4, so a(6) = 6*(p(6) - d(6)) = 6*(11 - 4) = 6*7 = 42.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Jan 18 2013
STATUS
approved