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A303189 a(n) = [x^n] Product_{k=1..n} (1 - (n - k + 1)*x^k). 3
1, -1, -1, 5, 7, 21, -94, -117, -404, -840, 3541, 4536, 14412, 31313, 72175, -249424, -262828, -930639, -1895460, -4441316, -8085972, 24112570, 26214408, 87131883, 180197979, 411759028, 748154122, 1525043990, -3554837744, -3210408245, -11955482059, -23817949142, -55221348072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..32.

EXAMPLE

a(0) = 1;

a(1) = [x^1] (1 - x) = -1;

a(2) = [x^2] (1 - 2*x)*(1 - x^2) = -1;

a(3) = [x^3] (1 - 3*x)*(1 - 2*x^2)*(1 - x^3) = 5;

a(4) = [x^4] (1 - 4*x)*(1 - 3*x^2)*(1 - 2*x^3)*(1 - x^4) = 7;

a(5) = [x^5] (1 - 5*x)*(1 - 4*x^2)*(1 - 3*x^3)*(1 - 2*x^4)*(1 - x^5) = 21, etc.

...

The table of coefficients of x^k in expansion of Product_{k=1..n} (1 - (n - k + 1)*x^k) begins:

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

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

n = 2:  1,  -2, (-1),  2,   0,   0   ...

n = 3:  1,  -3,  -2,  (5),  3,   2,  ...

n = 4:  1,  -4,  -3,  10,  (7), 10,  ...

n = 5:  1,  -5,  -4,  17,  13, (21), ...

MATHEMATICA

Table[SeriesCoefficient[Product[(1 - (n - k + 1) x^k), {k, 1, n}], {x, 0, n}], {n, 0, 32}]

CROSSREFS

Cf. A022661, A292132, A303173, A303175, A303188, A303190.

Sequence in context: A049114 A179189 A030735 * A162462 A165144 A084164

Adjacent sequences:  A303186 A303187 A303188 * A303190 A303191 A303192

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Apr 19 2018

STATUS

approved

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Last modified September 26 23:44 EDT 2022. Contains 357051 sequences. (Running on oeis4.)