cp's OEIS Frontend

A187913 Generalized Riordan array based on the Fine's numbers A000957.

%I A187913 #5 Mar 30 2012 18:59:28
%S A187913 1,0,1,1,1,1,2,4,1,1,6,10,5,2,1,18,32,13,9,2,1,57,100,44,28,10,3,1,
%T A187913 186,329,142,100,32,15,3,1,622,1101,480,344,119,55,16,4,1,2120,3761,
%U A187913 1640,1214,420,216,60,22,4,1,7338,13035,5698,4300,1517,810,243,92,23,5,1
%N A187913 Generalized Riordan array based on the Fine's numbers A000957.
%C A187913 First column is the Fine's numbers A000957. Row sums are A000958. Inverse binomial transform of A187914.
%F A187913 Let g(x)=(1+2x-sqrt(1-4x))/(2x(2+x)) be the g.f. of the Fine's numbers A000957. Then column k has
%F A187913 g.f. x^k*g(x)^(k+1)/(1-xg(x)-x^2g(x)^2)^floor((k+1)/2).
%e A187913 Triangle begins
%e A187913 1,
%e A187913 0, 1,
%e A187913 1, 1, 1,
%e A187913 2, 4, 1, 1,
%e A187913 6, 10, 5, 2, 1,
%e A187913 18, 32, 13, 9, 2, 1,
%e A187913 57, 100, 44, 28, 10, 3, 1,
%e A187913 186, 329, 142, 100, 32, 15, 3, 1,
%e A187913 622, 1101, 480, 344, 119, 55, 16, 4, 1,
%e A187913 2120, 3761, 1640, 1214, 420, 216, 60, 22, 4, 1,
%e A187913 7338, 13035, 5698, 4300, 1517, 810, 243, 92, 23, 5, 1
%e A187913 Production matrix is
%e A187913 0, 1,
%e A187913 1, 1, 1,
%e A187913 1, 2, 0, 1,
%e A187913 1, 2, 1, 1, 1,
%e A187913 1, 2, 1, 2, 0, 1,
%e A187913 1, 2, 1, 2, 1, 1, 1,
%e A187913 1, 2, 1, 2, 1, 2, 0, 1,
%e A187913 1, 2, 1, 2, 1, 2, 1, 1, 1,
%e A187913 1, 2, 1, 2, 1, 2, 1, 2, 0, 1
%e A187913 Thus
%e A187913 57=1.0+0.18+1.32+1.13+1.9+1.2+1.1;
%e A187913 100=1.18+1.32+2.13+2.9+2.2+2.1;
%e A187913 44=1.32+0.13+1.9+1.2+1.1
%K A187913 nonn,easy,tabl
%O A187913 0,7
%A A187913 _Paul Barry_, Mar 15 2011