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 A091540 Rescaled second column A091539 of array A091534 ((5,2)-Stirling2). 3
 1, 13, 184, 3040, 58360, 1283800, 31917760, 886123840, 27192323200, 914387689600, 33446228569600, 1322364153510400, 56203860301388800, 2555756347720576000, 123819357959385088000, 6367367706293321728000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS A certain difference of two triple factorial sequences. If offset 0: exponential (also called binomial) convolution of A091541 and A051606. LINKS G. C. Greubel, Table of n, a(n) for n = 2..380 FORMULA a(n)= (5*2/fac3(3*n-1))*A091539(n), n>=2, with fac3(3*n-1) := A008544(n) (triple factorials). E.g.f.: (1-2*x-(1-3*x)^(2/3))/(2*(1-3*x))= (1/2-x+int((1-3*x)^(-1/3), x))/(1-3*x). E.g.f. with offset 0: (3-2*(1-3*x)^(2/3))/(1-3*x)^3. a(n)=(fac3(3*n) - 3*fac3(3*n-2))/3! with fac3(3*n) := A032031(n)= n!*3^n and fac3(3*n-2) := A007559(n). a(n) ~ 3^(n-1) * n! / 2. - Vaclav Kotesovec, Aug 16 2018 MATHEMATICA Drop[With[{nmax = 50}, CoefficientList[Series[(1 - 2*x - (1 - 3*x)^(2/3))/(2*(1 - 3*x)), {x, 0, nmax}], x]*Range[0, nmax]!], 2] (* G. C. Greubel, Aug 15 2018 *) PROG (PARI) x='x+O('x^30); Vec(serlaplace((1 - 2*x - (1 - 3*x)^(2/3))/(2*(1 - 3*x)))) \\ G. C. Greubel, Aug 15 2018 (Magma) m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (3-2*(1-3*x)^(2/3))/(1-3*x)^3 )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018 CROSSREFS Cf. A091541. Sequence in context: A268413 A274345 A227503 * A057799 A057801 A094736 Adjacent sequences: A091537 A091538 A091539 * A091541 A091542 A091543 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Feb 13 2004 STATUS approved

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Last modified April 23 07:11 EDT 2024. Contains 371905 sequences. (Running on oeis4.)