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A363778
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} x^(j^2))^k.
4
1, 1, 0, 1, -1, 0, 1, -2, 1, 0, 1, -3, 3, -1, 0, 1, -4, 6, -4, 0, 0, 1, -5, 10, -10, 3, 1, 0, 1, -6, 15, -20, 12, 0, -2, 0, 1, -7, 21, -35, 31, -9, -5, 3, 0, 1, -8, 28, -56, 65, -36, -2, 12, -3, 0, 1, -9, 36, -84, 120, -96, 24, 24, -18, 1, 0, 1, -10, 45, -120, 203, -210, 105, 20, -54, 18, 2, 0
OFFSET
0,8
FORMULA
T(0,k) = 1; T(n,k) = -(k/n) * Sum_{j=1..n} A162552(j) * T(n-j,k).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, -1, -2, -3, -4, -5, -6, ...
0, 1, 3, 6, 10, 15, 21, ...
0, -1, -4, -10, -20, -35, -56, ...
0, 0, 3, 12, 31, 65, 120, ...
0, 1, 0, -9, -36, -96, -210, ...
0, -2, -5, -2, 24, 105, 294, ...
CROSSREFS
Columns k=0..3 give A000007, A317665, A363774, A363775.
Main diagonal gives A363780.
Sequence in context: A279594 A335162 A077593 * A213888 A119337 A213889
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Jun 21 2023
STATUS
approved