The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003576 Dowling numbers: e.g.f.: exp(x + (exp(b*x) - 1)/b) with b=4. 12
 1, 2, 8, 48, 352, 3008, 29440, 324096, 3947520, 52541440, 757260288, 11733385216, 194272854016, 3419584921600, 63707979972608, 1251489089060864, 25836869372608512, 558946705406427136, 12638569755079344128, 298003073694026432512, 7312035980392431353856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Muniru A Asiru, Table of n, a(n) for n = 0..230 Moussa Benoumhani, On Whitney numbers of Dowling lattices, Discrete Math. 159 (1996), no. 1-3, 13-33. FORMULA E.g.f.: exp(z + (exp(4*z) - 1)/4). G.f.: 1/Q(0), where Q(k) = 1 - 2*x*(2*k+1) - 2*x^2*(2*k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Sep 26 2013 a(n) = exp(-1/4) * Sum_{k>=0} (4*k + 1)^n / (4^k * k!). - Ilya Gutkovskiy, Apr 16 2020 MAPLE seq(coeff(series(factorial(n)*exp(z+(1/4)*exp(4*z)-(1/4)), z, n+1), z, n), n = 0 .. 20); # Muniru A Asiru, Feb 22 2019 MATHEMATICA With[{m=20, b=4}, CoefficientList[Series[Exp[x+(Exp[b*x]-1)/b], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Feb 22 2019 *) Table[Sum[Binomial[n, k] * 4^k * BellB[k, 1/4], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 17 2020 *) PROG (PARI) my(x='x+O('x^20)); b=4; Vec(serlaplace(exp(x+(exp(b*x)-1)/b))) \\ G. C. Greubel, Feb 22 2019 (MAGMA) m:=20; c:=4; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x+(Exp(c*x)-1)/c) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Feb 22 2019 (Sage) m = 20; b=4; 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 22 2019 CROSSREFS Cf. A000110 (b=1), A007405 (b=2), A003575 (b=3), this sequence (b=4), A003577 (b=5), A003578 (b=6), A003579 (b=7), A003580 (b=8), A003581 (b=9), A003582 (b=10). Sequence in context: A136722 A085615 A054726 * A225042 A326887 A095989 Adjacent sequences:  A003573 A003574 A003575 * A003577 A003578 A003579 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 15 19:43 EDT 2021. Contains 342977 sequences. (Running on oeis4.)