A394530 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals downwards, where A(n,k) = k^(n*(k-1)) - Sum_{j=1..k-1} k^(n*(k-1-j)) * j^n * A(n,j).

1, 0, 1, 0, 1, 1, 0, 4, 3, 1, 0, 28, 60, 7, 1, 0, 278, 3108, 646, 15, 1, 0, 3554, 304272, 237022, 6240, 31, 1, 0, 55382, 48129840, 223962842, 16144800, 57814, 63, 1, 0, 1015750, 11201299512, 435358129934, 147801031200, 1057628638, 526680, 127, 1

Offset

0,8

Links

Table of n, a(n) for n=0..44.

Formula

Sum_{j=1..k} j^n * A(n,j)/k^(n*j) = 1.

Example

Square array A(n,k) begins:
  1,  0,     0,          0,              0, ...
  1,  1,     4,         28,            278, ...
  1,  3,    60,       3108,         304272, ...
  1,  7,   646,     237022,      223962842, ...
  1, 15,  6240,   16144800,   147801031200, ...
  1, 31, 57814, 1057628638, 94200312330938, ...

Prog

(PARI) a(n, k) = k^(n*(k-1))-sum(j=1, k-1, k^(n*(k-1-j))*j^n*a(n, j));

Crossrefs

Rows n=1..2 give A374601, A394531.

Cf. A342202.

Sequence in context: A327069 A327334 A354794 * A355401 A195596 A332054

Adjacent sequences: A394527 A394528 A394529 * A394531 A394532 A394533

Keyword

nonn,tabl

Author

Seiichi Manyama, Mar 24 2026

Status

approved