# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a138106
Showing 1-1 of 1

%I A138106 #9 Apr 02 2019 08:06:57
%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,
%T A138106 210,-120,30,0,-1,-126,434,-630,490,-210,42,0,-1,254,-1008,1736,-1680,
%U A138106 980,-336,56,0,-1,-510,2286,-4536,5208,-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: {-1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,...}.
%C A138106 The Morse potential is identified with simple intermolecular energy to distance relationships.
%D A138106 A. Messiah, Quantum mechanics, vol. 2, p. 795, fig.XVIII.2, North Holland, 1969.
%H A138106 G. C. Greubel, <a href="/A138106/b138106.txt">Rows n = 1..100 of triangle, flattened</a>
%F A138106 p(x,t) = exp(x*t)*(exp(-2*t) - 2*exp(-t)) = Sum_{n>=0} P(x,n)*t^n/n!.
%e A138106 Triangle begins as:
%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;
%e A138106   .....
%t A138106 p[t_] = Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t]);
%t A138106 Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}];
%t A138106 Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]//Flatten
%K A138106 tabl,sign
%O A138106 1,4
%A A138106 _Roger L. Bagula_, May 03 2008
%E A138106 Edited by _G. C. Greubel_, Apr 01 2019

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE