%I A059297
%S A059297 1,0,1,0,2,1,0,3,6,1,0,4,24,12,1,0,5,80,90,20,1,0,6,240,540,240,
%T A059297 30,1,0,7,672,2835,2240,525,42,1,0,8,1792,13608,17920,7000,1008,
%U A059297 56,1,0,9,4608,61236,129024,78750,18144,1764,72,1,0,10,11520,262440
%N A059297 Triangle of idempotent numbers binomial(n,k)*k^(n-k), version 1.
%D A059297 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #43 and p. 135, 
               [3i'].
%H A059297 G. Duchamp, K. A. Penson, A. I. Solomon, A. Horzela and P. Blasiak, <a 
               href="http://arXiv.org/abs/quant-ph/0401126">One-parameter groups 
               and combinatorial physics</a>.
%F A059297 E.g.f.: exp(x*y*exp(y)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 
               18 2003
%e A059297 Triangle begins 1; 0, 1; 0, 2, 1; 0, 3, 6, 1; 0, 4, 24, 12, 1; ...
%Y A059297 There are 4 versions: A059297-A059300. Diagonals give A001788, A036216, 
               A040075, A050982, A002378, 3*A002417, etc. Row sums are A000248.
%Y A059297 Sequence in context: A145460 A035543 A105546 this_sequence A077874 A153007 
               A090683
%Y A059297 Adjacent sequences: A059294 A059295 A059296 this_sequence A059298 A059299 
               A059300
%K A059297 nonn,tabl
%O A059297 0,5
%A A059297 N. J. A. Sloane (njas(AT)research.att.com), Jan 25 2001