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Search: id:A137391
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| A137391 |
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Triangular sequence of coefficients from a Sheffer sequence expansion: f(t) = 1 + t + t^2; g(t) = t + t^2; p(t) = f[t]*Exp[x*g[t]];. |
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+0
1
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| 1, 1, 1, 2, 4, 1, 0, 12, 9, 1, 0, 24, 48, 16, 1, 0, 0, 180, 140, 25, 1, 0, 0, 360, 840, 330, 36, 1, 0, 0, 0, 3360, 2940, 672, 49, 1, 0, 0, 0, 6720, 18480, 8400, 1232, 64, 1, 0, 0, 0, 0, 75600, 75600, 20664, 2088, 81, 1, 0, 0, 0, 0, 151200, 483840, 252000, 45360, 3330
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums: {1, 2, 7, 22, 89, 346, 1567, 7022, 34897, 174034, 935831}
Basic Sheffer functions( coefficients one):
f(t)*(t-1)=t^3-1;
g(t)=t*(t+1)=f(t)-1;
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REFERENCES
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Weisstein, Eric W. "Sheffer Sequence." >http://mathworld.wolfram.com/ShefferSequence.html
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FORMULA
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f(t) = 1 + t + t^2; g(t) = t + t^2; p(t) = f[t]*Exp[x*g[t]]; p(t)=Sum[s(x,n]*t^n/n!,{n,0,Infinity}] Out[n,m]=n!*Coefficient(s(x,n))
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EXAMPLE
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{1},
{1, 1},
{2, 4, 1},
{0, 12, 9, 1},
{0, 24, 48, 16, 1},
{0, 0, 180, 140, 25, 1},
{0, 0, 360, 840, 330, 36, 1},
{0, 0, 0, 3360, 2940, 672, 49, 1},
{0, 0, 0, 6720, 18480, 8400, 1232, 64, 1},
{0, 0, 0, 0, 75600, 75600, 20664, 2088, 81, 1},
{0, 0, 0, 0, 151200, 483840, 252000, 45360, 3330, 100, 1}
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MATHEMATICA
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Clear[p, f, g] f[t_] = 1 + t + t^2; g[t_] = t + t^2; p[t_] = f[t]*Exp[x*g[t]]; Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A137388 A137389 A137390 this_sequence A137392 A137393 A137394
Sequence in context: A067849 A152433 A094344 this_sequence A059817 A099803 A010741
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Apr 10 2008
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