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).

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

Seiichi Manyama, Antidiagonals n = 0..59, flattened

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

Adjacent sequences: A306626 A306627 A306628 * A306630 A306631 A306632

Keyword

sign,tabl

Author

Seiichi Manyama, Mar 02 2019

Status

approved