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

%I A187555 #14 Feb 28 2018 11:32:01
%S A187555 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 A187555 1275,90,1,0,5040,37044,56840,25725,3675,147,1,0,40320,365904,735392,
%U A187555 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 A187555 Triangle read by rows, defined by T(n,k)=binomial(n,k)*|Stirling1(n,k)|, 0<=k<=n.
%H A187555 Vincenzo Librandi, <a href="/A187555/b187555.txt">Table of n, a(n) for n = 0..2020</a>
%F A187555 a(n,k) = binomial(n,k)*A132393(n,k).
%e A187555 Triangle begins:
%e A187555 1
%e A187555 0,1
%e A187555 0,2,1
%e A187555 0,6,9,1
%e A187555 0,24,66,24,1
%e A187555 0,120,500,350,50,1
%e A187555 0,720,4110,4500,1275,90,1
%e A187555 0,5040,37044,56840,25725,3675,147,1
%e A187555 0,40320,365904,735392,473830,109760,9016,224,1
%p A187555 seq(seq(binomial(n,k)*abs(combinat[stirling1](n,k)),k=0..n),n=0..8);
%t A187555 Flatten[Table[
%t A187555   Table[Binomial[n, k] Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 10}], 1]
%o A187555 (Maxima) create_list(binomial(n,k)*abs(stirling1(n,k)),n,0,10,k,0,n);
%Y A187555 Row sum sequence is A211210.
%K A187555 nonn,easy,tabl
%O A187555 0,5
%A A187555 _Emanuele Munarini_, Mar 11 2011
%E A187555 Edited by _Olivier Gérard_, Oct 23 2012