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A003576 Dowling numbers: e.g.f.: exp(x + (exp(b*x) - 1)/b) with b=4. 9
1, 2, 8, 48, 352, 3008, 29440, 324096, 3947520, 52541440, 757260288, 11733385216, 194272854016, 3419584921600, 63707979972608, 1251489089060864, 25836869372608512, 558946705406427136 (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

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 *)

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<x>:=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

N. J. A. Sloane

STATUS

approved

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Last modified October 20 15:15 EDT 2019. Contains 328267 sequences. (Running on oeis4.)