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 A066189 Sum of all partitions of n into distinct parts. 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 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 *) CROSSREFS Row sums of A026793, A118457, A246688, A325537. Cf. A015723, A022629, A066186, A147655, A325504, A325505, A325506, A325513, A325515, A325537. Sequence in context: A128913 A093005 A049818 * A278834 A306906 A174658 Adjacent sequences:  A066186 A066187 A066188 * A066190 A066191 A066192 KEYWORD easy,nonn AUTHOR Wouter Meeussen, Dec 15 2001 STATUS approved

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Last modified April 9 15:21 EDT 2020. Contains 333359 sequences. (Running on oeis4.)