A276552 -id:A276552 - cp's OEIS frontend

A276554 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-x^j)^(j*k) in powers of x.

1, 1, 0, 1, -1, 0, 1, -2, -2, 0, 1, -3, -3, -1, 0, 1, -4, -3, 2, 0, 0, 1, -5, -2, 8, 6, 4, 0, 1, -6, 0, 16, 12, 12, 4, 0, 1, -7, 3, 25, 13, 9, 1, 7, 0, 1, -8, 7, 34, 5, -12, -29, -10, 3, 0, 1, -9, 12, 42, -15, -51, -78, -54, -32, -2, 0, 1, -10, 18, 48, -49, -102

Offset: 0

Seiichi Manyama, Apr 10 2017

			Square array begins:
   1,  1,  1,  1,  1, ...
   0, -1, -2, -3, -4, ...
   0, -2, -3, -3, -2, ...
   0, -1,  2,  8, 16, ...
   0,  0,  6, 12, 13, ...

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

Columns k=0-5 give: A000007, A073592, A276551, A276552, A316463, A316464.
Main diagonal gives A281267.
Antidiagonal sums give A299211.
Cf. A255961, A277938.

G.f. of column k: Product_{j>=1} (1-x^j)^(j*k).

A276551 Convolution square of A073592.

Original entry on oeis.org

1, -2, -3, 2, 6, 12, 1, -10, -32, -46, -24, 18, 96, 168, 213, 124, -61, -386, -734, -992, -957, -386, 685, 2288, 3939, 5158, 5012, 2930, -1853, -8888, -17283, -24782, -28312, -24422, -9825, 16674, 54197, 96584, 134729, 153718, 138624, 73438, -49526, -228614

Offset: 0

Seiichi Manyama, Apr 10 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Column k=2 of A276554.

Product_{k>0} (1-x^k)^(k*m): A161870 (m=-2), A073592 (m=1), this sequence (m=2), A276552 (m=3).

G.f.: Product_{k>0} (1-x^k)^(k*2).

G.f.: exp(-2*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018

cp's OEIS Frontend

A276554 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-x^j)^(j*k) in powers of x.

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