A187555 Triangle read by rows, defined by T(n,k)=binomial(n,k)*|Stirling1(n,k)|, 0<=k<=n.

1, 0, 1, 0, 2, 1, 0, 6, 9, 1, 0, 24, 66, 24, 1, 0, 120, 500, 350, 50, 1, 0, 720, 4110, 4500, 1275, 90, 1, 0, 5040, 37044, 56840, 25725, 3675, 147, 1, 0, 40320, 365904, 735392, 473830, 109760, 9016, 224, 1, 0, 362880, 3945024, 9922416, 8477784, 2828574, 381024, 19656, 324, 1, 0, 3628800, 46195920, 140724000, 151972800, 67869900, 13287330, 1134000, 39150, 450, 1

Offset: 0

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins:
1
0,1
0,2,1
0,6,9,1
0,24,66,24,1
0,120,500,350,50,1
0,720,4110,4500,1275,90,1
0,5040,37044,56840,25725,3675,147,1
0,40320,365904,735392,473830,109760,9016,224,1
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2020

Crossrefs

Row sum sequence is A211210.

Programs

Maple

seq(seq(binomial(n,k)*abs(combinat[stirling1](n,k)),k=0..n),n=0..8);

Mathematica

Flatten[Table[
  Table[Binomial[n, k] Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 10}], 1]

Maxima

create_list(binomial(n,k)*abs(stirling1(n,k)),n,0,10,k,0,n);

Formula

a(n,k) = binomial(n,k)*A132393(n,k).

Extensions

Edited by Olivier Gérard, Oct 23 2012