A348649 Odd numbers in the triangle of Stirling numbers of the second kind (A008277).

1, 1, 1, 1, 3, 1, 1, 7, 1, 1, 15, 25, 1, 1, 31, 65, 15, 1, 1, 63, 301, 21, 1, 1, 127, 1701, 1, 1, 255, 3025, 6951, 1, 1, 511, 34105, 42525, 22827, 45, 1, 1, 1023, 28501, 179487, 63987, 1155, 55, 1, 1, 2047, 611501, 159027, 22275, 1705, 1, 1, 4095, 261625, 7508501, 39325, 2431, 1

Offset: 1

Author

Rémy Sigrist, Oct 27 2021

Keywords

• nonn
• tabf

Comments

We take the odd values in A008277, as they appear, with duplicates.

For any n >= 1, the n-th row has A007306(n) terms.

Examples

			As an irregular table, the first rows are:
     1:    1;
     2:    1, 1;
     3:    1, 3, 1;
     4:    1, 7, 1;
     5:    1, 15, 25, 1;
     6:    1, 31, 65, 15, 1;
     7:    1, 63, 301, 21, 1;
     8:    1, 127, 1701, 1;
     9:    1, 255, 3025, 6951, 1;
    10:    1, 511, 34105, 42525, 22827, 45, 1;
    11:    1, 1023, 28501, 179487, 63987, 1155, 55, 1;
    ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10057 (rows for n = 1..331, flattened)
• Rémy Sigrist, Logarithmic scatterplot of the first 35000 terms
• Index entries for sequences related to Stirling numbers

Crossrefs

See A014421, A014428, A014450, A014459 for similar sequences.

Cf. A007306, A008277, A348650 (even numbers).

Programs

PARI

row(n) = select(v -> v%2==1, vector(n, k, stirling(n, k, 2)))