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A306629
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} (j!)^k * x^j).
2
1, 1, -1, 1, -1, 0, 1, -1, -1, 0, 1, -1, -3, -3, 0, 1, -1, -7, -29, -13, 0, 1, -1, -15, -201, -499, -71, 0, 1, -1, -31, -1265, -13351, -13101, -461, 0, 1, -1, -63, -7713, -328975, -1697705, -486131, -3447, 0, 1, -1, -127, -46529, -7946143, -206659569, -369575303, -24266797, -29093, 0
OFFSET
0,13
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = -Sum_{j=1..n} (j!)^k * A(n-j,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, ...
0, -1, -3, -7, -15, ...
0, -3, -29, -201, -1265, ...
0, -13, -499, -13351, -328975, ...
0, -71, -13101, -1697705, -206659569, ...
0, -461, -486131, -369575303, -268312660751, ...
CROSSREFS
Columns 1-3 give A167894, A113871, A316862.
Rows 0-2 give A000012, (-1)*A000012, (-1)*A000225.
Main diagonal gives A306630.
Sequence in context: A288395 A288644 A172169 * A185282 A193470 A102752
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Mar 02 2019
STATUS
approved