A244489 Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n,j)*Stirling_2(j,k)*Bell(n-j), where Bell(n) = A000110(n), for n >= 1, 0 <= k <= n-1.

1, 2, 3, 5, 10, 6, 15, 37, 31, 10, 52, 151, 160, 75, 15, 203, 674, 856, 520, 155, 21, 877, 3263, 4802, 3556, 1400, 287, 28, 4140, 17007, 28337, 24626, 11991, 3290, 490, 36, 21147, 94828, 175896, 174805, 101031, 34671, 6972, 786, 45, 115975, 562595, 1146931, 1279240, 853315, 350889, 88977, 13620, 1200, 55

Offset: 1

Author

N. J. A. Sloane, Jul 04 2014

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1
2 3
5 10 6
15 37 31 10
52 151 160 75 15
203 674 856 520 155 21
877 3263 4802 3556 1400 287 28
4140 17007 28337 24626 11991 3290 490 36
...
		

Links

• J. East, R. D. Gray, Idempotent generators in finite partition monoids and related semigroups, arXiv preprint arXiv:1404.2359 [math.GR], 2014.

Crossrefs

Same as A049020 (which is the main entry for this triangle) except the present sequence has an extra 1 at the end of each row. - R. J. Mathar and N. J. A. Sloane, May 17 2016

Programs

Mathematica

T[n_, k_] := Sum[Binomial[n, j] StirlingS2[j, k] BellB[n-j], {j, k, n}];
Table[T[n, k], {n, 1, 10}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Oct 09 2018 *)