Search: id:A089278
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%I A089278
%S A089278 1,1,3,1,15,24,7,405,2268,2500,2,405,6048,20000,16875,11,7425,266112,2000000,
%T A089278 4640625,3176523,143,312741,25474176,390000000,1879453125,3344878719,1927561216,
%U A089278 143,995085,178319232,5250000000,46986328125,163899057231,236126248960
%V A089278 1,-1,3,1,-15,24,-7,405,-2268,2500,2,-405,6048,-20000,16875,-11,7425,-266112,
               2000000,
%W A089278 -4640625,3176523,143,-312741,25474176,-390000000,1879453125,-3344878719,
               1927561216,
%X A089278 -143,995085,-178319232,5250000000,-46986328125,163899057231,-236126248960
%N A089278 Coefficient triangle for computation of column numbers of triangle A071951 
               (Legendre-Stirling).
%C A089278 The k-th column sequence A071951(n+k,k), n>=0, is sum(a(k,p)*(p*(p+1))^n,
               p=1..k)/A089500(k), k>=1.
%H A089278 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A089278.text">
               First 7 rows</a>.
%F A089278 a(n, m)= A089500(n)*(((-1)^(m+n))*(2*m+1)*((m*(m+1))^n)/((m+n+1)!*(n-m)!)).
%e A089278 [1]; [ -1,3]; [1,-15,24]; [ -7,405,-2268,2500]; ...
%e A089278 Sequence A071951(n+3,3)= A016309(n)= [1,20,292,...] has a(n)=
%e A089278 (1*(1*2)^n - 15*(2*3)^n + 24*(3*4)^n)/10.
%Y A089278 Sequence in context: A113378 A156289 A095922 this_sequence A087071 A053485 
               A143565
%Y A089278 Adjacent sequences: A089275 A089276 A089277 this_sequence A089279 A089280 
               A089281
%K A089278 sign,tabl
%O A089278 1,3
%A A089278 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Nov 07 2003

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