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 A003580 Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=8. 11
 1, 2, 12, 120, 1424, 19488, 307904, 5539712, 111259904, 2454487552, 58847153152, 1522019629056, 42209521995776, 1248370355347456, 39186678731423744, 1300179383923212288, 45436201241711542272, 1667242078056889843712, 64063345344029286727680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Muniru A Asiru, Table of n, a(n) for n = 0..190 Moussa Benoumhani, On Whitney numbers of Dowling lattices, Discrete Math. 159 (1996), no. 1-3, 13-33. FORMULA E.g.f.: exp(x + (exp(8*x) - 1)/8). a(n) = exp(-1/8) * Sum_{k>=0} (8*k + 1)^n / (8^k * k!). - Ilya Gutkovskiy, Apr 16 2020 MAPLE seq(coeff(series(factorial(n)*exp(z+(1/8)*exp(8*z)-(1/8)), z, n+1), z, n), n = 0 .. 20); # Muniru A Asiru, Feb 24 2019 MATHEMATICA With[{m=20, b=8}, CoefficientList[Series[Exp[x +(Exp[b*x]-1)/b], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Feb 24 2019 *) Table[Sum[Binomial[n, k] * 8^k * BellB[k, 1/8], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 17 2020 *) PROG (PARI) my(x='x+O('x^20)); b=8; Vec(serlaplace(exp(x +(exp(b*x)-1)/b))) \\ G. C. Greubel, Feb 24 2019 (MAGMA) m:=20; c:=8; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x +(Exp(c*x)-1)/c) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Feb 24 2019 (Sage) m = 20; b=8; T = taylor(exp(x + (exp(b*x) -1)/b), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Feb 24 2019 CROSSREFS Cf. A000110 (b=1), A007405 (b=2), A003575 (b=3), A003576 (b=4), A003577 (b=5), A003578 (b=6), A003579 (b=7), this sequence (b=8), A003581 (b=9), A003582 (b=10). Sequence in context: A286629 A329851 A127112 * A052580 A134095 A204042 Adjacent sequences:  A003577 A003578 A003579 * A003581 A003582 A003583 KEYWORD nonn AUTHOR EXTENSIONS Name clarified by Muniru A Asiru, Feb 24 2019 STATUS approved

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Last modified January 20 16:49 EST 2021. Contains 340303 sequences. (Running on oeis4.)