A383064 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of e.g.f. Sum_{j>=0} (j+1)^k * (-log(1-x))^j / j!.

1, 1, 1, 1, 2, 2, 1, 4, 5, 6, 1, 8, 13, 17, 24, 1, 16, 35, 51, 74, 120, 1, 32, 97, 161, 244, 394, 720, 1, 64, 275, 531, 854, 1392, 2484, 5040, 1, 128, 793, 1817, 3148, 5248, 9260, 18108, 40320, 1, 256, 2315, 6411, 12134, 20940, 36966, 70508, 149904, 362880

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Formula

See A344639.

Example

Square array begins:
    1,    1,    1,     1,      1,      1,       1, ...
    1,    2,    4,     8,     16,     32,      64, ...
    2,    5,   13,    35,     97,    275,     793, ...
    6,   17,   51,   161,    531,   1817,    6411, ...
   24,   74,  244,   854,   3148,  12134,   48604, ...
  120,  394, 1392,  5248,  20940,  87784,  384252, ...
  720, 2484, 9260, 36966, 156680, 699894, 3274640, ...

Prog

(PARI) a(n, k) = sum(j=0, n, j!*abs(stirling(n+1, j+1, 1))*stirling(k+1, j+1, 2));

Crossrefs

Mirror of A344639.

Main diagonal gives A192563.

Sequence in context: A218580 A259697 A330664 * A330843 A115313 A048942

Adjacent sequences: A383061 A383062 A383063 * A383065 A383066 A383067

Keyword

nonn,tabl

Author

Seiichi Manyama, Apr 15 2025

Status

approved