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A066189
Sum of all partitions of n into distinct parts.
27
0, 1, 2, 6, 8, 15, 24, 35, 48, 72, 100, 132, 180, 234, 308, 405, 512, 646, 828, 1026, 1280, 1596, 1958, 2392, 2928, 3550, 4290, 5184, 6216, 7424, 8880, 10540, 12480, 14784, 17408, 20475, 24048, 28120, 32832, 38298, 44520, 51660, 59892, 69230, 79904
OFFSET
0,3
LINKS
FORMULA
G.f.: sum(n>=1, n*q^(n-1)/(1+q^n) ) * prod(n>=1, 1+q^n ). - Joerg Arndt, Aug 03 2011
a(n) = n * A000009(n). - Vaclav Kotesovec, Sep 25 2016
G.f.: x*f'(x), where f(x) = Product_{k>=1} (1 + x^k). - Vaclav Kotesovec, Nov 21 2016
a(n) = A056239(A325506(n)). - Gus Wiseman, May 09 2019
EXAMPLE
The strict integer partitions of 6 are {(6), (5,1), (4,2), (3,2,1)} with sum 6+5+1+4+2+3+2+1 = 24. - Gus Wiseman, May 09 2019
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i>n, [0$2],
b(n, i+1)+(p-> p+[0, i*p[1]])(b(n-i, i+1))))
end:
a:= n-> b(n, 1)[2]:
seq(a(n), n=0..80); # Alois P. Heinz, Sep 01 2014
MATHEMATICA
PartitionsQ[ Range[ 60 ] ]Range[ 60 ]
nmax=60; CoefficientList[Series[x*D[Product[1+x^k, {k, 1, nmax}], x], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 21 2016 *)
KEYWORD
easy,nonn
AUTHOR
Wouter Meeussen, Dec 15 2001
STATUS
approved