A137597 Triangle read by rows: A008277 * A007318.

1, 2, 1, 5, 5, 1, 15, 22, 9, 1, 52, 99, 61, 14, 1, 203, 471, 385, 135, 20, 1, 877, 2386, 2416, 1140, 260, 27, 1, 4140, 12867, 15470, 9156, 2835, 455, 35, 1, 21147, 73681, 102215, 72590, 28441, 6230, 742, 44, 1

Offset: 1

Author

Gary W. Adamson, Jan 29 2008

Keywords

• nonn
• tabl

Comments

Row sums = A035009 starting (1, 3, 11, 47, 227, ...).

Examples

			First few rows of the triangle:
    1;
    2,   1;
    5,   5,   1;
   15,  22,   9,   1;
   52,  99,  61,  14,  1;
  203, 471, 385, 135, 20, 1;
  ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows n = 1..150, flattened)
• Zhanar Berikkyzy, Pamela E. Harris, Anna Pun, Catherine Yan, and Chenchen Zhao, Combinatorial Identities for Vacillating Tableaux, arXiv:2308.14183 [math.CO], 2023. See p. 16.

Crossrefs

Cf. A035009, A008277.

Cf. A126350.

Programs

Maple

T:= (n, k)-> add(Stirling2(n, j)*binomial(j-1, k-1), j=k..n):
seq(seq(T(n, k), k=1..n), n=1..10);  # Alois P. Heinz, Sep 03 2019

Mathematica

Table[Sum[StirlingS2[n, j]*Binomial[j - 1, k - 1], {j, k, n}], {n, 9}, {k, n}] // Flatten (* Michael De Vlieger, Aug 31 2023 *)

Formula

A008277 * A007318 as infinite lower triangular matrices.