A362926 Triangle read by rows: A113547 without its main diagonal.

1, 1, 2, 1, 4, 5, 1, 8, 13, 15, 1, 16, 35, 47, 52, 1, 32, 97, 153, 188, 203, 1, 64, 275, 515, 706, 825, 877, 1, 128, 793, 1785, 2744, 3479, 3937, 4140, 1, 256, 2315, 6347, 11002, 15177, 18313, 20270, 21147, 1, 512, 6817, 23073, 45368, 68303, 88033, 102678, 111835, 115975, 1, 1024, 20195, 85475, 191866, 316305, 436297, 536882, 610989, 657423, 678570

Offset

1,3

Comments

A variant of A113547 and A362924. See those entries for further information.

Links

Table of n, a(n) for n=1..66.

Example

Triangle begins:
  [1],
  [1, 2],
  [1, 4, 5],
  [1, 8, 13, 15],
  [1, 16, 35, 47, 52],
  [1, 32, 97, 153, 188, 203],
  [1, 64, 275, 515, 706, 825, 877],
  [1, 128, 793, 1785, 2744, 3479, 3937, 4140],
  [1, 256, 2315, 6347, 11002, 15177, 18313, 20270, 21147],
  ...

Mathematica

A362926[n_, m_]:=Sum[StirlingS2[m-1, k-1]k^(n-m+1), {k, m}];
Table[A362926[n, m], {n, 15}, {m, n}] (* Paolo Xausa, Dec 02 2023 *)

Crossrefs

Cf. A113547, A362924.

Sequence in context: A134248 A248670 A080935 * A102661 A121574 A117317

Adjacent sequences: A362923 A362924 A362925 * A362927 A362928 A362929

Keyword

nonn,tabl

Author

N. J. A. Sloane, Aug 11 2023, based on an email from Don Knuth.

Extensions

Name corrected by Paolo Xausa, Dec 02 2023

Status

approved