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, 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

Author

Omar E. Pol, Jan 18 2013

Keywords

• nonn
• easy

Examples

			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)
-----------------------------------------------------
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

Cf. A000005, A000041, A038040, A066186, A144300, A220477.

Formula

a(n) = n*(A000041(n) - A000005(n)) = A066186(n) - A038040(n) = n*A144300(n).