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 A309084 a(n) = exp(3) * Sum_{k>=0} (-3)^k*k^n/k!. 3
 1, -3, 6, -3, -21, 24, 195, -111, -3072, -4053, 57003, 277854, -697539, -12261567, -29861778, 371727465, 3511027599, 2028432480, -188521156857, -1470389129931, 1655487186864, 121873222577823, 915525253963023, -2095901567014530, -103715912230195863, -836215492271268459 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..571 FORMULA G.f.: Sum_{j>=0} (-3)^j*x^j / Product_{k=1..j} (1 - k*x). E.g.f.: exp(3*(1 - exp(x))). a(n) = Sum_{k=0..n} (-3)^k * Stirling2(n,k). MATHEMATICA Table[Exp[3] Sum[(-3)^k k^n/k!, {k, 0, Infinity}], {n, 0, 25}] Table[BellB[n, -3], {n, 0, 25}] nmax = 25; CoefficientList[Series[Sum[(-3)^j x^j/Product[(1 - k x), {k, 1, j}] , {j, 0, nmax}], {x, 0, nmax}], x] nmax = 25; CoefficientList[Series[Exp[3 (1 - Exp[x])], {x, 0, nmax}], x] Range[0, nmax]! PROG (MAGMA) [1] cat [(&+[((-3)^k*StirlingSecond(m, k)):k in [0..m]]):m in [1..25]]; // Marius A. Burtea, Jul 27 2019 CROSSREFS Column k = 3 of A292861. Cf. A000587, A027710, A213170, A309085, A317996. Sequence in context: A205865 A085881 A265480 * A288092 A127574 A169842 Adjacent sequences:  A309081 A309082 A309083 * A309085 A309086 A309087 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jul 11 2019 STATUS approved

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Last modified October 16 08:45 EDT 2019. Contains 328056 sequences. (Running on oeis4.)