|
|
A318364
|
|
Expansion of e.g.f. exp(x*exp(x)/(1 - x)).
|
|
2
|
|
|
1, 1, 5, 28, 197, 1676, 16597, 186796, 2350105, 32634928, 495207881, 8144456684, 144204493765, 2733218222944, 55188182951917, 1182163846918156, 26765995313355953, 638508459302742464, 16002492517241163793, 420279349847440766284, 11540406000681962458141, 330624627443307824367616
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(0) = 1; a(n) = Sum_{k=1..n} A007526(k)*binomial(n-1,k-1)*a(n-k).
a(n) ~ exp(1/4 - 3*exp(1)/2 + 2*exp(1/2)*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - Vaclav Kotesovec, Aug 25 2018
|
|
MAPLE
|
a:=series(exp(x*exp(x)/(1 - x)), x=0, 22): seq(n!*coeff(a, x, n), n=0..21); # Paolo P. Lava, Mar 26 2019
|
|
MATHEMATICA
|
nmax = 21; CoefficientList[Series[Exp[x Exp[x]/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Floor[Exp[1] k! - 1] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 21}]
|
|
PROG
|
(PARI) x = 'x + O('x^25); Vec(serlaplace(exp(x*exp(x)/(1 - x)))) \\ Michel Marcus, Aug 25 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|