%I A156139
%S A156139 1,1,1,1,6,1,1,23,28,1,1,76,250,145,1,1,237,1608,2475,876,1,1,722,8802,
%T A156139 26847,25056,6139,1,1,2179,43872,231057,418806,268477,49120,1,1,6552,
%U A156139 205994,1725621,5285520,6486205,3077730,442089,1,1,19673,928808
%N A156139 A triangular recursion: A(n,k)=(2*n - k - 1)*A(n - 1, k - 1) + (k + 1)*A(n 
               - 1, k)
%C A156139 Row sums are:
%C A156139 {1, 2, 8, 53, 473, 5198, 67568, 1013513, 17229713, 327364538,...}.
%D A156139 Leonard M. Smiley,"Completion of a Rational Function Sequence of Carlitz,
               http://www.math.uaa.alaska.edu/~smiley/BSfront.html,page 2.
%F A156139 A(n,k)=(2*n - k - 1)*A(n - 1, k - 1) + (k + 1)*A(n - 1, k)
%e A156139 {1},
%e A156139 {1, 1},
%e A156139 {1, 6, 1},
%e A156139 {1, 23, 28, 1},
%e A156139 {1, 76, 250, 145, 1},
%e A156139 {1, 237, 1608, 2475, 876, 1},
%e A156139 {1, 722, 8802, 26847, 25056, 6139, 1},
%e A156139 {1, 2179, 43872, 231057, 418806, 268477, 49120, 1},
%e A156139 {1, 6552, 205994, 1725621, 5285520, 6486205, 3077730, 442089, 1},
%e A156139 {1, 19673, 928808, 11718015, 55871814, 114115195, 102456300, 37833831, 
               4420900, 1}
%t A156139 A[n_, 1] := 1; A[n_, n_] := 1;
%t A156139 A[n_, k_] := (2*n - k - 1)*A[n - 1, k - 1] + (k + 1)*A[n - 1, k];
%t A156139 TableForm[Table[A[n, k], {n, 10}, {k, n}], TableAlignments -> Right];
%t A156139 Table[Table[A[n, k], {k, n}], {n, 10}];
%t A156139 Flatten[%]
%Y A156139 Sequence in context: A152936 A152969 A060187 this_sequence A155863 A035348 
               A140945
%Y A156139 Adjacent sequences: A156136 A156137 A156138 this_sequence A156140 A156141 
               A156142
%K A156139 nonn,tabl,uned
%O A156139 1,5
%A A156139 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 04 2009