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A154923 A symmetrical triangle sequence made from A154537:q(x,n)= Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]); p(x,n)=q(x,n)+x^n*q(1/x,n); t(n,m)=coefficients(p(x,n)).

%I A154923 #4 Sep 16 2015 19:38:33
%S A154923 2,3,3,5,16,5,9,62,62,9,17,208,464,208,17,33,642,2680,2680,642,33,65,
%T A154923 1880,13404,24320,13404,1880,65,129,5322,62188,180488,180488,62188,
%U A154923 5322,129,257,14752,280144,1209600,1858752,1209600,280144,14752,257,513
%N A154923 A symmetrical triangle sequence made from A154537:q(x,n)= Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]); p(x,n)=q(x,n)+x^n*q(1/x,n); t(n,m)=coefficients(p(x,n)).
%C A154923 Row sums are:
%C A154923 {2, 6, 26, 142, 914, 6710, 55018, 496254, 4868258, 51483878, 582795578,...}
%F A154923 q(x,n)= Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]);
%F A154923 p(x,n)=q(x,n)+x^n*q(1/x,n);
%F A154923 t(n,m)=coefficients(p(x,n)).
%e A154923 {2},
%e A154923 {3, 3},
%e A154923 {5, 16, 5},
%e A154923 {9, 62, 62, 9},
%e A154923 {17, 208, 464, 208, 17},
%e A154923 {33, 642, 2680, 2680, 642, 33},
%e A154923 {65, 1880, 13404, 24320, 13404, 1880, 65},
%e A154923 {129, 5322, 62188, 180488, 180488, 62188, 5322, 129},
%e A154923 {257, 14752, 280144, 1209600, 1858752, 1209600, 280144, 14752, 257},
%e A154923 {513, 40418, 1262544, 7828640, 16609824, 16609824, 7828640, 1262544, 40418, 513},
%e A154923 {1025, 110248, 5787604, 50950400, 140957728, 187181568, 140957728, 50950400, 5787604, 110248, 1025}
%t A154923 p[x_, n_] = Sum[(2*m + 1)^n*x^m/m!, {m, 0, Infinity}]/(Exp[x]);
%t A154923 Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}]'
%t A154923 Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]
%t A154923 + Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}]'
%t A154923 Flatten[%]
%Y A154923 A154537
%K A154923 nonn,tabl,uned
%O A154923 0,1
%A A154923 _Roger L. Bagula_, Jan 17 2009