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A321565 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^9. 52

%I

%S 1,-513,19684,-261633,1953126,-10097892,40353608,-133955073,387440173,

%T -1001953638,2357947692,-5149983972,10604499374,-20701400904,

%U 38445332184,-68584996353,118587876498,-198756808749,322687697780,-511002214758

%N a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^9.

%H Seiichi Manyama, <a href="/A321565/b321565.txt">Table of n, a(n) for n = 1..10000</a>

%H J. W. L. Glaisher, <a href="https://books.google.com/books?id=bLs9AQAAMAAJ&amp;pg=RA1-PA1">On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares</a>, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).

%H <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>

%F G.f.: Sum_{k>=1} (-1)^(k+1)*k^9*x^k/(1 + x^k). - _Ilya Gutkovskiy_, Dec 22 2018

%t CoefficientList[Series[Sum[(-1)^(k+1) k^9 x^k/(1+x^k),{k,20}],{x,0,20}],x] (* _Harvey P. Dale_, Apr 09 2019 *)

%o (PARI) apply( A321565(n)=sumdiv(n, d, (-1)^(n\d-d)*d^9), [1..30]) \\ _M. F. Hasler_, Nov 26 2018

%Y Column k=9 of A322083.

%Y Cf. A321543 - A321564, A321807 - A321836 for similar sequences.

%K sign,mult

%O 1,2

%A _N. J. A. Sloane_, Nov 23 2018

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Last modified May 26 17:16 EDT 2020. Contains 334630 sequences. (Running on oeis4.)