%I A138106
%S A138106 1,0,1,2,0,1,6,6,0,1,14,24,12,0,1,30,70,60,20,0,1,62,180,210,120,30,0,
               1,
%T A138106 126,434,630,490,210,42,0,1,254,1008,1736,1680,980,336,56,0,1,510,2286,
               4536,
%U A138106 5208,3780,1764,504,72,0,1,1022,5100,11430,15120,13020,7560,2940,720,90,
               0,1
%V A138106 -1,0,-1,2,0,-1,-6,6,0,-1,14,-24,12,0,-1,-30,70,-60,20,0,-1,62,-180,210,
               -120,30,0,-1,
%W A138106 -126,434,-630,490,-210,42,0,-1,254,-1008,1736,-1680,980,-336,56,0,-1,
               -510,2286,-4536,
%X A138106 5208,-3780,1764,-504,72,0,-1,1022,-5100,11430,-15120,13020,-7560,2940,
               -720,90,0,-1
%N A138106 A triangular sequence of coefficients based on the expansion of a Morse 
               potential type function: p(x,t)=Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t]).
%C A138106 Row sums are:
%C A138106 {-1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1};
%C A138106 The Morse potential is identified with simple
%C A138106 intermolecular energy to distance relationships.
%D A138106 A. Messiah, Quantum mechanics, vol. 2, p. 795, fig.XVIII.2, North Holland, 
               1969.
%F A138106 p(x,t)=Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t])=sum(P(x,n)*t^n/n!,{n,0,Infinity}); 
               Out_n,m=Coefficients(P(x,n)).
%e A138106 {-1},
%e A138106 {0, -1},
%e A138106 {2, 0, -1},
%e A138106 {-6, 6, 0, -1},
%e A138106 {14, -24, 12, 0, -1},
%e A138106 {-30, 70, -60, 20, 0, -1},
%e A138106 {62, -180, 210, -120, 30, 0, -1},
%e A138106 {-126, 434, -630, 490, -210, 42, 0, -1},
%e A138106 {254, -1008, 1736, -1680,980, -336, 56, 0, -1},
%e A138106 {-510, 2286, -4536, 5208, -3780, 1764, -504, 72, 0, -1},
%e A138106 {1022, -5100, 11430, -15120, 13020, -7560, 2940, -720, 90, 0, -1}
%t A138106 p[t_] = Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t]); Table[ ExpandAll[n!*SeriesCoefficient[ 
               Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ 
               Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
%Y A138106 Sequence in context: A114709 A089949 A085845 this_sequence A131689 A114329 
               A101371
%Y A138106 Adjacent sequences: A138103 A138104 A138105 this_sequence A138107 A138108 
               A138109
%K A138106 uned,tabl,sign
%O A138106 1,4
%A A138106 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 03 2008