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A293305
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} (-1)^j*j*x^(j*i)).
6
1, 1, 0, 1, -1, 0, 1, -1, -1, 0, 1, -1, 1, 0, 0, 1, -1, 1, 0, 0, 0, 1, -1, 1, -3, 0, 1, 0, 1, -1, 1, -3, 0, -3, 0, 0, 1, -1, 1, -3, 4, 0, 4, 1, 0, 1, -1, 1, -3, 4, 0, 4, -3, 0, 0, 1, -1, 1, -3, 4, -5, 0, -3, 4, 0, 0, 1, -1, 1, -3, 4, -5, 0, -7, -2, -2, 0, 0, 1, -1, 1
OFFSET
0,25
LINKS
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
0, -1, -1, -1, -1, ...
0, -1, 1, 1, 1, ...
0, 0, 0, -3, -3, ...
0, 0, 0, 0, 4, ...
0, 1, -3, 0, 0, ...
MATHEMATICA
nmax = 12;
col[k_] := col[k] = Product[1+Sum[(-1)^j*j*x^(i*j), {j, 1, k}], {i, 1, 2 nmax}] + O[x]^(2 nmax) // CoefficientList[#, x]&;
A[n_, k_] := If[n == 0, 1, If[k == 0, 0, col[k][[n+1]]]];
Table[A[n-k, k], {n, 0, nmax}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Feb 21 2021 *)
CROSSREFS
Columns k=0..2 give A000007, A010815, A293072.
Rows n=0 gives A000012.
Main diagonal gives A293306.
Sequence in context: A323878 A046094 A055976 * A316896 A230626 A363946
KEYWORD
sign,tabl,look
AUTHOR
Seiichi Manyama, Oct 05 2017
STATUS
approved