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A292166 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j^k*x^j). 7
1, 1, -1, 1, -1, -1, 1, -1, -2, 0, 1, -1, -4, -1, 0, 1, -1, -8, -5, -1, 1, 1, -1, -16, -19, -7, 5, 0, 1, -1, -32, -65, -37, 27, 1, 1, 1, -1, -64, -211, -175, 155, 17, 13, 0, 1, -1, -128, -665, -781, 927, 205, 167, 4, 0, 1, -1, -256, -2059, -3367, 5675, 2129 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*j/d)) * A(n-j,k) for n > 0. - Seiichi Manyama, Nov 02 2017

EXAMPLE

Square array begins:

    1,  1,  1,   1,    1, ...

   -1, -1, -1,  -1,   -1, ...

   -1, -2, -4,  -8,  -16, ...

    0, -1, -5, -19,  -65, ...

    0, -1, -7, -37, -175, ...

CROSSREFS

Columns k=0..2 give A010815, A022661, A292164.

Rows n=0..2 give A000012, (-1)*A000012, (-1)*A000079.

Main diagonal gives A292167.

Sequence in context: A110298 A144740 A283272 * A282192 A049501 A102564

Adjacent sequences:  A292163 A292164 A292165 * A292167 A292168 A292169

KEYWORD

sign,look,tabl

AUTHOR

Seiichi Manyama, Sep 10 2017

STATUS

approved

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Last modified December 14 15:01 EST 2019. Contains 329979 sequences. (Running on oeis4.)