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 A137387 Triangular sequence from coefficients of the expansion of p(x,t)=Exp[2*x*t]*t/(1 - t). 0
 0, 1, 2, 4, 6, 12, 12, 24, 48, 48, 32, 120, 240, 240, 160, 80, 720, 1440, 1440, 960, 480, 192, 5040, 10080, 10080, 6720, 3360, 1344, 448, 40320, 80640, 80640, 53760, 26880, 10752, 3584, 1024, 362880, 725760, 725760, 483840, 241920, 96768, 32256, 9216 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums = A066534. REFERENCES Terrell Hill, Statistical Mechanics, Dover, 1987, page 417 LINKS FORMULA p(x,t)=Exp[2*x*t]*t/(1 - t)=Sum[P(x,n)*t6n/n!,{n,1,Infinity}]; out_n,m=n!*Coefficients(P(x,n)). EXAMPLE {0}, {1}, {2, 4}, {6, 12, 12}, {24, 48, 48, 32}, {120, 240, 240, 160, 80}, {720, 1440, 1440, 960, 480, 192}, {5040, 10080, 10080, 6720, 3360, 1344, 448}, {40320, 80640, 80640, 53760, 26880, 10752, 3584, 1024}, {362880, 725760, 725760, 483840, 241920, 96768, 32256, 9216, 2304}, {3628800, 7257600, 7257600, 4838400, 2419200, 967680, 322560, 92160, 23040,5120} MATHEMATICA p[t_] = Exp[2*x*t]*t/(1 - 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] CROSSREFS Cf. A066534. Sequence in context: A061799 A076868 A056793 * A137394 A062856 A056371 Adjacent sequences:  A137384 A137385 A137386 * A137388 A137389 A137390 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Apr 26 2008 STATUS approved

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Last modified July 23 22:49 EDT 2019. Contains 325278 sequences. (Running on oeis4.)