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Triangle read by rows, defined by T(n,k)=binomial(n,k)*|Stirling1(n,k)|, 0<=k<=n.
2

%I #14 Feb 28 2018 11:32:01

%S 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,

%T 1275,90,1,0,5040,37044,56840,25725,3675,147,1,0,40320,365904,735392,

%U 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

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

%H Vincenzo Librandi, <a href="/A187555/b187555.txt">Table of n, a(n) for n = 0..2020</a>

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

%e Triangle begins:

%e 1

%e 0,1

%e 0,2,1

%e 0,6,9,1

%e 0,24,66,24,1

%e 0,120,500,350,50,1

%e 0,720,4110,4500,1275,90,1

%e 0,5040,37044,56840,25725,3675,147,1

%e 0,40320,365904,735392,473830,109760,9016,224,1

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

%t Flatten[Table[

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

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

%Y Row sum sequence is A211210.

%K nonn,easy,tabl

%O 0,5

%A _Emanuele Munarini_, Mar 11 2011

%E Edited by _Olivier GĂ©rard_, Oct 23 2012