A171684 Triangle T(n,k) which contains 8*n!*2^floor((n+1)/2) times the coefficient [t^n x^k] exp(t*x)/(7 + exp(4*t)) in row n, column k.
1, -1, 2, -3, -2, 2, -11, -18, -6, 4, 30, -44, -36, -8, 4, 866, 300, -220, -120, -20, 8, 3858, 5196, 900, -440, -180, -24, 8, -23654, 54012, 36372, 4200, -1540, -504, -56, 16, -722760, -189232, 216048, 96992, 8400, -2464, -672, -64, 16, -10842136, -13009680, -1703088, 1296288, 436464, 30240, -7392, -1728, -144, 32
Offset: 0
Examples
The triangle starts in row n=0 with columns 0<=k <=n as
1;
-1, 2;
-3, -2, 2;
-11, -18, -6, 4;
30, -44, -36, -8, 4;
866, 300, -220, -120, -20, 8;
3858, 5196, 900, -440, -180, -24, 8;
-23654, 54012, 36372, 4200, -1540, -504, -56, 16;
-722760, -189232, 216048, 96992, 8400, -2464, -672, -64, 16;
...
Programs
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Mathematica
Clear[p, g, m, a]; m = 2; p[t_] = 2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[2^m*t]) Table[ FullSimplify[ExpandAll[2^ Floor[(n + 1)/2]*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], {n, 0, 10}] a = Table[CoefficientList[FullSimplify[ExpandAll[2^Floor[(n + 1)/2]*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}] Flatten[a]
Extensions
Number of variables in use reduced from 4 to 2, keyword:tabl added - The Assoc. Eds. of the OEIS, Oct 20 2010
Comments