|
| |
|
|
A003582
|
|
Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=10.
|
|
9
|
|
|
|
1, 2, 14, 168, 2356, 37832, 701464, 14866848, 352943376, 9219925792, 261954304224, 8033968939648, 264411579439936, 9288709762556032, 346608927301622144, 13680000261825018368, 569006722158124974336
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Muniru A Asiru, Table of n, a(n) for n = 0..180
Moussa Benoumhani, On Whitney numbers of Dowling lattices, Discrete Math. 159 (1996), no. 1-3, 13-33.
|
|
|
FORMULA
|
E.g.f.: exp(x + (exp(10*x) - 1)/10).
|
|
|
MAPLE
|
seq(coeff(series(factorial(n)*exp(z+(1/10)*exp(10*z)-(1/10)), z, n+1), z, n), n = 0 .. 20); # Muniru A Asiru, Feb 24 2019
|
|
|
MATHEMATICA
|
With[{m=20, b=10}, CoefficientList[Series[Exp[x +(Exp[b*x]-1)/b], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Feb 24 2019 *)
|
|
|
PROG
|
(PARI) my(x='x+O('x^20)); b=10; Vec(serlaplace(exp(x +(exp(b*x)-1)/b))) \\ G. C. Greubel, Feb 24 2019
(MAGMA) m:=20; c:=10; R<x>:=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=10; 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), A003580 (b=8), A003581 (b=9), this sequence (b=10).
Sequence in context: A209937 A245896 A124215 * A277373 A084946 A047055
Adjacent sequences: A003579 A003580 A003581 * A003583 A003584 A003585
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
Name clarified by Muniru A Asiru, Feb 24 2019
|
|
|
STATUS
|
approved
|
| |
|
|
