A360548
E.g.f. satisfies A(x) = x * exp( 2*(x + A(x)) ).
Original entry on oeis.org
0, 1, 8, 96, 1792, 46080, 1511424, 60325888, 2837970944, 153778913280, 9432255692800, 646039266656256, 48874810528235520, 4047655951598092288, 364221261622538141696, 35384754572803304325120, 3691411033400626898796544, 411569264258973944034361344
Offset: 0
-
A360548 := proc(n)
add((2*k)^(n-1)*binomial(n,k),k=1..n) ;
end proc:
seq(A360548(n),n=0..60) ; # R. J. Mathar, Mar 12 2023
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-2*x*exp(2*x))/2)))
-
a(n) = sum(k=1, n, (2*k)^(n-1)*binomial(n, k));
A360545
E.g.f. satisfies A(x) = x * exp( 3*(x + A(x))/2 ).
Original entry on oeis.org
0, 1, 6, 54, 756, 14580, 358668, 10736712, 378823392, 15395255280, 708217959600, 36380741745744, 2064234271203360, 128214974795177088, 8652900673357097472, 630483717450225530880, 49330027417316557012992, 4124992361928178722764544
Offset: 0
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-2*lambertw(-3*x/2*exp(3*x/2))/3)))
-
a(n) = sum(k=1, n, (3*k/2)^(n-1)*binomial(n, k));
A216858
Number of connected functions from {1,2,...,n} into a subset of {1,2,...,n} summed over all subsets.
Original entry on oeis.org
0, 1, 5, 38, 422, 6184, 112632, 2453296, 62202800, 1799623296, 58507176320, 2111633645824, 83777729991936, 3624054557443072, 169759643117603840, 8560585769442662400, 462387289560368764928, 26633435981686107701248, 1629609677806398679646208, 105555926477075661655441408, 7215930505311133152120995840
Offset: 0
-
nn=20; a=-ProductLog[-x Exp[x] ]; Range[0,nn]! CoefficientList[Series[Log[1/(1-a)], {x,0,nn}], x]
-
x='x+O('x^30); concat([0], Vec(serlaplace(log(1/(1+ lambertw(-x*exp(x))))))) \\ G. C. Greubel, Nov 16 2017
A360433
E.g.f. satisfies A(x) = x * exp(A(x) + x^3).
Original entry on oeis.org
0, 1, 2, 9, 88, 865, 11016, 173929, 3227792, 69010785, 1670970160, 45198840841, 1350754588008, 44196732194641, 1571453132115608, 60331412278617705, 2487385479819549856, 109608035124514365121, 5140910415583354887648, 255708987797133857518345
Offset: 0