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A299033 a(n) = n! * [x^n] Product_{k>=1} (1 - x^k)^(n/k). 3
1, -1, 0, 15, -136, 885, -4896, 43085, -787200, 7775271, 326355200, -22138191801, 781498160640, -18924340012435, 239123351330304, 5915023788331125, -568462201562300416, 25327272129182225295, -795994018378027868160, 15538852668590468027711 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(n) = n! * [x^n] exp(-n*Sum_{k>=1} d(k)*x^k/k), where d(k) is the number of divisors of k (A000005).

EXAMPLE

The table of coefficients of x^k in expansion of e.g.f. Product_{k>=1} (1 - x^k)^(n/k) begins:

n = 0: (1),  0,    0,    0,     0,      0,      0,  ...

n = 1:  1, (-1),  -1,    1,    -1,     41,   -131,  ...

n = 2:  1,  -2,   (0),   8,    -4,     72,   -704,  ...

n = 3:  1,  -3,    3,  (15),  -45,     63,  -1539,  ...

n = 4:  1,  -4,    8,   16, (-136),   224,  -1856,  ...

n = 5:  1,  -5,   15,    5,  -265,   (885), -2075,  ...

n = 6:  1,  -6,   24,  -24,  -396,   2376, (-4896), ...

MATHEMATICA

Table[n! SeriesCoefficient[Product[(1 - x^k)^(n/k), {k, 1, n}], {x, 0, n}], {n, 0, 19}]

CROSSREFS

Cf. A000005, A028343, A281267, A299034.

Sequence in context: A254409 A155648 A126536 * A030056 A225978 A175707

Adjacent sequences:  A299030 A299031 A299032 * A299034 A299035 A299036

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Feb 01 2018

STATUS

approved

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Last modified August 2 20:38 EDT 2021. Contains 346428 sequences. (Running on oeis4.)