A355427 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - Sum_{j=1..k} (exp(j*x) - 1)/j).

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 11, 13, 0, 1, 4, 24, 89, 75, 0, 1, 5, 42, 284, 959, 541, 0, 1, 6, 65, 654, 4476, 12917, 4683, 0, 1, 7, 93, 1255, 13564, 88178, 208781, 47293, 0, 1, 8, 126, 2143, 32275, 351634, 2084564, 3937019, 545835, 0

Offset

0,8

Links

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

Formula

T(0,k) = 1 and T(n,k) = Sum_{i=1..n} (Sum_{j=1..k} j^(i-1)) * binomial(n,i) * T(n-i,k) for n > 0.

Example

Square array begins:
  1,   1,     1,     1,      1,       1, ...
  0,   1,     2,     3,      4,       5, ...
  0,   3,    11,    24,     42,      65, ...
  0,  13,    89,   284,    654,    1255, ...
  0,  75,   959,  4476,  13564,   32275, ...
  0, 541, 12917, 88178, 351634, 1037479, ...

Crossrefs

Columns k=0..3 give A000007, A000670, A355425, A355426.

Main diagonal gives A355428.

Cf. A306024, A320253.

Sequence in context: A349971 A340986 A340798 * A122078 A292783 A320354

Adjacent sequences: A355424 A355425 A355426 * A355428 A355429 A355430

Keyword

nonn,tabl

Author

Seiichi Manyama, Jul 01 2022

Status

approved