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A321565 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^9. 52
1, -513, 19684, -261633, 1953126, -10097892, 40353608, -133955073, 387440173, -1001953638, 2357947692, -5149983972, 10604499374, -20701400904, 38445332184, -68584996353, 118587876498, -198756808749, 322687697780, -511002214758 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).

Index entries for sequences mentioned by Glaisher

FORMULA

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

MATHEMATICA

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 *)

PROG

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

CROSSREFS

Column k=9 of A322083.

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

Sequence in context: A111344 A230188 A223651 * A017681 A013957 A294304

Adjacent sequences:  A321562 A321563 A321564 * A321566 A321567 A321568

KEYWORD

sign,mult

AUTHOR

N. J. A. Sloane, Nov 23 2018

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)